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Biblioteca

MARC Lista (tabellare)
Analysis of reaction-diffusion models with the Taxis mechanism / / Yuanyuan Ke, Jing Li, Yifu Wang
Analysis of reaction-diffusion models with the Taxis mechanism / / Yuanyuan Ke, Jing Li, Yifu Wang
Autore Ke Yuanyuan
Pubbl/distr/stampa Singapore, : Springer Nature, 2022
Descrizione fisica 1 online resource (ix, 411 pages) : illustrations (some color)
Altri autori (Persone) LiJing
WangYifu
Collana Financial Mathematics and Fintech
Soggetto topico Boundary value problems
Chemotaxis - Mathematical models
Navier-Stokes equations
Problemes de contorn
Quimiotaxi
Models matemàtics
Equacions de Navier-Stokes
Soggetto genere / forma Llibres electrònics
Soggetto non controllato Reaction-Diffusion
Chemotaxis
Haptotaxis
Navier-Stokes
Cancer invasion
Coral fertilization
Sensity-suppressed motility
Oncolytic virotherapy
Foraging scrounging interplay
ISBN 981-19-3763-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1. Large time behavior of solutions to the chemotaxis-fluid Chapter 2. Global existence in Keller Segel Navier Stokes system involving tensor-valued sensitivity Chapter 3. Large time behavior of solutions to chemotaxis haptotaxis models Chapter 4. Large time behavior of Keller Segel (Navier) Stokes system modeling coral fertilization Chapter 5. Qualitative properties to density-suppressed motility models Chapter 6. Large time behavior of multi-taxis cross-diffusion system
Record Nr. UNISA-996485660903316
Ke Yuanyuan  
Singapore, : Springer Nature, 2022
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Analysis of reaction-diffusion models with the Taxis mechanism / / Yuanyuan Ke, Jing Li, Yifu Wang
Analysis of reaction-diffusion models with the Taxis mechanism / / Yuanyuan Ke, Jing Li, Yifu Wang
Autore Ke Yuanyuan
Pubbl/distr/stampa Singapore, : Springer Nature, 2022
Descrizione fisica 1 online resource (ix, 411 pages) : illustrations (some color)
Altri autori (Persone) LiJing
WangYifu
Collana Financial Mathematics and Fintech
Soggetto topico Boundary value problems
Chemotaxis - Mathematical models
Navier-Stokes equations
Problemes de contorn
Quimiotaxi
Models matemàtics
Equacions de Navier-Stokes
Soggetto genere / forma Llibres electrònics
Soggetto non controllato Reaction-Diffusion
Chemotaxis
Haptotaxis
Navier-Stokes
Cancer invasion
Coral fertilization
Sensity-suppressed motility
Oncolytic virotherapy
Foraging scrounging interplay
ISBN 981-19-3763-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1. Large time behavior of solutions to the chemotaxis-fluid Chapter 2. Global existence in Keller Segel Navier Stokes system involving tensor-valued sensitivity Chapter 3. Large time behavior of solutions to chemotaxis haptotaxis models Chapter 4. Large time behavior of Keller Segel (Navier) Stokes system modeling coral fertilization Chapter 5. Qualitative properties to density-suppressed motility models Chapter 6. Large time behavior of multi-taxis cross-diffusion system
Record Nr. UNINA-9910588786303321
Ke Yuanyuan  
Singapore, : Springer Nature, 2022
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic theory of dynamic boundary value problems in irregular domains / / Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov
Asymptotic theory of dynamic boundary value problems in irregular domains / / Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov
Autore Korikov Dmitrii
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2021]
Descrizione fisica 1 online resource (xi, 399 pages)
Disciplina 515.353
Collana Operator Theory: Advances and Applications
Soggetto topico Boundary value problems - Asymptotic theory
Problemes de contorn
Soggetto genere / forma Llibres electrònics
ISBN 3-030-65372-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 2 Wave Equation in Domains with Edges -- 2.1 Dirichlet Problem for the Wave Equation -- 2.1.1 Function Spaces in a Wedge and in a Cone -- 2.1.2 Problem in a Wedge: Problem with Parameter in a Cone: Existence of Solutions -- 2.1.3 Weighted Combined Estimates -- 2.1.4 Operators in the Scale of Weighted Spaces -- 2.1.5 Asymptotics of Solutions Near the Vertex of a Cone or Near the Edge of a Wedge -- 2.1.6 Explicit Formulas for the Coefficients in Asymptotics -- 2.1.7 Problem in a Bounded Domain with Conical Points -- 2.1.8 Problem in a Bounded Domain: Asymptotics of Solutions Near an Internal Point -- 2.2 Neumann Problem for the Wave Equation -- 2.2.1 Statement of the Problem: Preliminaries -- 2.2.2 Weighted Combined Estimates for Solutions to Problem (2.138), (2.139) -- 2.2.3 Operator of the Boundary Value Problem in a Cone -- 2.2.4 Boundary Value Problem in a Cone in the Scale of Weighted Spaces -- 2.2.5 Asymptotic Expansions of Solutions to the Problem in a Cone -- 2.2.6 Problem in a Wedge -- 2.2.7 Explicit Formulas for the Coefficients in Asymptotics -- 2.2.8 Problem in a Bounded Domain with Conical Points -- 3 Hyperbolic Systems in Domains with Conical Points -- 3.1 Cauchy-Dirichlet Problem -- 3.1.1 Combined Estimate for Solutions of the Problem in a Cone -- 3.1.2 Operator of the Boundary Value Problem in a Cone: The Existence and Uniqueness of Solutions -- 3.1.3 The Boundary Value Problem in a Cone in the Scale of Weighted Spaces -- 3.1.4 Asymptotics of Solutions of the Problem in a Cone -- 3.1.5 The Problem in a Wedge -- 3.2 Neumann Problem -- 3.2.1 The Model Problems in a Cone: A Strong Solution -- 3.2.2 Weighted Estimates of Solutions of the Problem with Parameter in a Cone -- 3.2.3 The Problem with Parameter in a Cone: A Scale of Weighted Spaces -- 3.2.4 The Asymptotics of Solutions.
3.2.5 A Bounded Domain with a Conical Point -- 4 Elastodynamics in Domains with Edges -- 4.1 Introduction -- 4.2 Homogeneous Energy Estimates on Solutions of Boundary Value Problems with Parameter in a Wedge -- 4.3 Nonhomogeneous Energy Estimates for Solutions of Boundary Value Problems with Parameter in a Wedge -- 4.3.1 Estimates on Solutions with Dirichlet BoundaryCondition -- 4.3.2 Estimates on Solutions with Neumann Boundary Condition -- 4.4 Strong Solutions -- 4.4.1 The Dirichlet Problem with Homogeneous Energy Estimate in a Wedge -- 4.4.2 The Dirichlet Problem with Nonhomogeneous Energy Estimate in a Wedge -- 4.4.3 The Neumann Problem in a Wedge -- 4.5 Weighted a priori Estimates for Solutions of Boundary Value Problems with Parameter in a Wedge -- 4.5.1 Estimates of Solutions with DirichletBoundary Condition -- 4.5.2 Estimate on Solutions with Neumann Boundary Condition in the Case dim K> -- 2 -- 4.5.3 Estimates of Solutions with Neumann Boundary Condition for dim K=2 -- 4.6 Boundary Value Problem in a Cone in a Scaleof Weighted Spaces -- 4.6.1 On the Asymptotics of Solutions of Elliptic Problems in a Cone -- 4.6.2 Strong Solutions -- 4.6.3 The Operator of Problem (4.105), (4.106)in a Scale of Weighted Spaces -- 4.6.4 Asymptotics of Solutions of the Problem in a Cone -- 4.7 On the Time-Dependent Problem in a Wedge -- 4.8 Energy Estimates on Solutions in a Bounded Domain -- 4.9 Weighted Estimates in a Bounded Domain with Edge -- 5 On Dynamic Maxwell System in Domains with Edges -- 5.1 The Problems in a Cone and in a Bounded Domain with Conical Point -- 5.1.1 Preliminaries: Statement of the Problem -- 5.1.2 Operator Pencil -- 5.1.3 A Global Energy Estimate -- 5.1.4 A Combined Weighted Estimate -- 5.1.5 The Operator of Problem in a Scaleof Weighted Spaces -- 5.1.6 The Asymptotics of Solutions.
5.1.7 Nonstationary Problem in the Cylinders Q and Q -- 5.1.8 Explicit Formulas of ws,k and Ws,k for the Problem in K -- 5.2 The Problem in a Wedge -- 5.2.1 Preliminaries: Statement of the Problem -- 5.2.2 Operator Pencil -- 5.2.3 On Properties of the Operator A(D) -- 5.2.4 Estimates of Solutions to Problems in a Wedge and in an Angle -- 5.2.5 The Operators of Problems in K -- 5.2.6 The Problem in the Cylinder T -- 5.2.7 Explicit Formulas for the Coefficients in the Asymptotics of Solutions of the Problem in T -- 5.2.8 Connection Between the Augmented and Non-augmented Maxwell Systems -- 6 Schroedinger and Germain-Lagrange Equations in a Domain with Corners -- 6.1 Schroedinger Equation -- 6.2 Germain-Lagrange Equation with Simply Supported Boundary Conditions -- 6.2.1 Combined Estimates -- 6.2.2 Asymptotics of Solutions -- 6.3 Germain-Lagrange Equation with Clamped BoundaryConditions -- 6.3.1 Problem in the Wedge: Problem with Parameter in a Sector-Existence of Solutions -- 6.3.2 Weighted Combined Estimates -- 6.3.3 Operators in the Scale of Weighted Spaces -- 6.3.4 Asymptotics of Solutions -- 6.3.5 Problem in a Bounded Domain with Corners -- 7 Asymptotics of Solutions to Wave Equation in Singularly Perturbed Domains -- 7.1 Asymptotics of Solutions to Wave Equation in a Domain with Small Cavity -- 7.1.1 Statement of Problem: Principal Term of Asymptotics -- 7.1.2 Estimate of the Remainder -- 7.1.3 Full Asymptotic Expansion -- 7.2 Asymptotics of Solutions to Wave Equation in a Domain with ``Smoothed'' Conical Point -- 8 Asymptotics of Solutions to Non-stationary Maxwell System in a Domain with Small Cavities -- 8.1 Elliptic Extension of Maxwell System with Parameter τ -- 8.2 Operator Pencil -- 8.3 The First Limit Problem -- 8.4 The Second Limit Problem -- 8.5 Asymptotics Principal Term of Solution to Extended Problem.
8.6 Asymptotic Series for Solution to Extended Problem -- 8.6.1 Asymptotics for Solutions to Non-extended Maxwell System -- 8.7 Non-stationary Maxwell System -- 8.7.1 Statement of Problem -- 8.7.2 Preliminary Description of Asymptotics for Solutions to Extended Problem -- 8.7.3 Principal Term of Asymptotics for Solutions to Problem (8.111), (8.112) -- 8.7.4 Proof of Theorem 8.7.4 -- 8.7.5 Estimate of the Remainder ũ1(·,τ,) for |τ|≤ρ0 -- 8.7.6 Estimate of the Functions u(·,τ,) and u0(·,τ,) for |τ|> -- ρ0 -- 8.7.7 Return to Extended Hyperbolic Problem -- 8.7.8 Return to Non-stationary Maxwell System Under Compatibility Conditions -- 8.8 Asymptotic Series as 0 for Solutions to Hyperbolic Problem -- 8.8.1 Estimates of Coefficients and Remaindersin (8.88), (8.89) -- 8.8.2 Estimate, Uniform with Respect to τ, of the Remainder ũN+1(·,τ,)in the Expansion (8.100) -- 8.8.3 Return to Non-extended Maxwell System (8.1) in (8.100), (8.101) -- 8.8.4 Complete Asymptotic Expansion of Solutions to Problem (8.111), (8.112) -- 8.9 Stationary Maxwell System with Impedance BoundaryConditions -- 8.10 Asymptotics for Solutions to Problem (8.192), (8.193) -- 8.10.1 Principal Term of Asymptotics -- 8.10.2 Estimate of the Remainder -- 8.10.3 Complete Asymptotic Expansion -- 8.10.4 Return to the Non-extended Maxwell System -- 8.11 Non-stationary Maxwell System with Impedance Boundary Conditions -- 8.12 Generalization to the Case of a Domain with Several SmallCavities -- Bibliographical Sketch -- References.
Record Nr. UNISA-996466545803316
Korikov Dmitrii  
Cham, Switzerland : , : Birkhäuser, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Asymptotic theory of dynamic boundary value problems in irregular domains / / Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov
Asymptotic theory of dynamic boundary value problems in irregular domains / / Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov
Autore Korikov Dmitrii
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2021]
Descrizione fisica 1 online resource (xi, 399 pages)
Disciplina 515.353
Collana Operator Theory: Advances and Applications
Soggetto topico Boundary value problems - Asymptotic theory
Problemes de contorn
Soggetto genere / forma Llibres electrònics
ISBN 3-030-65372-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 2 Wave Equation in Domains with Edges -- 2.1 Dirichlet Problem for the Wave Equation -- 2.1.1 Function Spaces in a Wedge and in a Cone -- 2.1.2 Problem in a Wedge: Problem with Parameter in a Cone: Existence of Solutions -- 2.1.3 Weighted Combined Estimates -- 2.1.4 Operators in the Scale of Weighted Spaces -- 2.1.5 Asymptotics of Solutions Near the Vertex of a Cone or Near the Edge of a Wedge -- 2.1.6 Explicit Formulas for the Coefficients in Asymptotics -- 2.1.7 Problem in a Bounded Domain with Conical Points -- 2.1.8 Problem in a Bounded Domain: Asymptotics of Solutions Near an Internal Point -- 2.2 Neumann Problem for the Wave Equation -- 2.2.1 Statement of the Problem: Preliminaries -- 2.2.2 Weighted Combined Estimates for Solutions to Problem (2.138), (2.139) -- 2.2.3 Operator of the Boundary Value Problem in a Cone -- 2.2.4 Boundary Value Problem in a Cone in the Scale of Weighted Spaces -- 2.2.5 Asymptotic Expansions of Solutions to the Problem in a Cone -- 2.2.6 Problem in a Wedge -- 2.2.7 Explicit Formulas for the Coefficients in Asymptotics -- 2.2.8 Problem in a Bounded Domain with Conical Points -- 3 Hyperbolic Systems in Domains with Conical Points -- 3.1 Cauchy-Dirichlet Problem -- 3.1.1 Combined Estimate for Solutions of the Problem in a Cone -- 3.1.2 Operator of the Boundary Value Problem in a Cone: The Existence and Uniqueness of Solutions -- 3.1.3 The Boundary Value Problem in a Cone in the Scale of Weighted Spaces -- 3.1.4 Asymptotics of Solutions of the Problem in a Cone -- 3.1.5 The Problem in a Wedge -- 3.2 Neumann Problem -- 3.2.1 The Model Problems in a Cone: A Strong Solution -- 3.2.2 Weighted Estimates of Solutions of the Problem with Parameter in a Cone -- 3.2.3 The Problem with Parameter in a Cone: A Scale of Weighted Spaces -- 3.2.4 The Asymptotics of Solutions.
3.2.5 A Bounded Domain with a Conical Point -- 4 Elastodynamics in Domains with Edges -- 4.1 Introduction -- 4.2 Homogeneous Energy Estimates on Solutions of Boundary Value Problems with Parameter in a Wedge -- 4.3 Nonhomogeneous Energy Estimates for Solutions of Boundary Value Problems with Parameter in a Wedge -- 4.3.1 Estimates on Solutions with Dirichlet BoundaryCondition -- 4.3.2 Estimates on Solutions with Neumann Boundary Condition -- 4.4 Strong Solutions -- 4.4.1 The Dirichlet Problem with Homogeneous Energy Estimate in a Wedge -- 4.4.2 The Dirichlet Problem with Nonhomogeneous Energy Estimate in a Wedge -- 4.4.3 The Neumann Problem in a Wedge -- 4.5 Weighted a priori Estimates for Solutions of Boundary Value Problems with Parameter in a Wedge -- 4.5.1 Estimates of Solutions with DirichletBoundary Condition -- 4.5.2 Estimate on Solutions with Neumann Boundary Condition in the Case dim K> -- 2 -- 4.5.3 Estimates of Solutions with Neumann Boundary Condition for dim K=2 -- 4.6 Boundary Value Problem in a Cone in a Scaleof Weighted Spaces -- 4.6.1 On the Asymptotics of Solutions of Elliptic Problems in a Cone -- 4.6.2 Strong Solutions -- 4.6.3 The Operator of Problem (4.105), (4.106)in a Scale of Weighted Spaces -- 4.6.4 Asymptotics of Solutions of the Problem in a Cone -- 4.7 On the Time-Dependent Problem in a Wedge -- 4.8 Energy Estimates on Solutions in a Bounded Domain -- 4.9 Weighted Estimates in a Bounded Domain with Edge -- 5 On Dynamic Maxwell System in Domains with Edges -- 5.1 The Problems in a Cone and in a Bounded Domain with Conical Point -- 5.1.1 Preliminaries: Statement of the Problem -- 5.1.2 Operator Pencil -- 5.1.3 A Global Energy Estimate -- 5.1.4 A Combined Weighted Estimate -- 5.1.5 The Operator of Problem in a Scaleof Weighted Spaces -- 5.1.6 The Asymptotics of Solutions.
5.1.7 Nonstationary Problem in the Cylinders Q and Q -- 5.1.8 Explicit Formulas of ws,k and Ws,k for the Problem in K -- 5.2 The Problem in a Wedge -- 5.2.1 Preliminaries: Statement of the Problem -- 5.2.2 Operator Pencil -- 5.2.3 On Properties of the Operator A(D) -- 5.2.4 Estimates of Solutions to Problems in a Wedge and in an Angle -- 5.2.5 The Operators of Problems in K -- 5.2.6 The Problem in the Cylinder T -- 5.2.7 Explicit Formulas for the Coefficients in the Asymptotics of Solutions of the Problem in T -- 5.2.8 Connection Between the Augmented and Non-augmented Maxwell Systems -- 6 Schroedinger and Germain-Lagrange Equations in a Domain with Corners -- 6.1 Schroedinger Equation -- 6.2 Germain-Lagrange Equation with Simply Supported Boundary Conditions -- 6.2.1 Combined Estimates -- 6.2.2 Asymptotics of Solutions -- 6.3 Germain-Lagrange Equation with Clamped BoundaryConditions -- 6.3.1 Problem in the Wedge: Problem with Parameter in a Sector-Existence of Solutions -- 6.3.2 Weighted Combined Estimates -- 6.3.3 Operators in the Scale of Weighted Spaces -- 6.3.4 Asymptotics of Solutions -- 6.3.5 Problem in a Bounded Domain with Corners -- 7 Asymptotics of Solutions to Wave Equation in Singularly Perturbed Domains -- 7.1 Asymptotics of Solutions to Wave Equation in a Domain with Small Cavity -- 7.1.1 Statement of Problem: Principal Term of Asymptotics -- 7.1.2 Estimate of the Remainder -- 7.1.3 Full Asymptotic Expansion -- 7.2 Asymptotics of Solutions to Wave Equation in a Domain with ``Smoothed'' Conical Point -- 8 Asymptotics of Solutions to Non-stationary Maxwell System in a Domain with Small Cavities -- 8.1 Elliptic Extension of Maxwell System with Parameter τ -- 8.2 Operator Pencil -- 8.3 The First Limit Problem -- 8.4 The Second Limit Problem -- 8.5 Asymptotics Principal Term of Solution to Extended Problem.
8.6 Asymptotic Series for Solution to Extended Problem -- 8.6.1 Asymptotics for Solutions to Non-extended Maxwell System -- 8.7 Non-stationary Maxwell System -- 8.7.1 Statement of Problem -- 8.7.2 Preliminary Description of Asymptotics for Solutions to Extended Problem -- 8.7.3 Principal Term of Asymptotics for Solutions to Problem (8.111), (8.112) -- 8.7.4 Proof of Theorem 8.7.4 -- 8.7.5 Estimate of the Remainder ũ1(·,τ,) for |τ|≤ρ0 -- 8.7.6 Estimate of the Functions u(·,τ,) and u0(·,τ,) for |τ|> -- ρ0 -- 8.7.7 Return to Extended Hyperbolic Problem -- 8.7.8 Return to Non-stationary Maxwell System Under Compatibility Conditions -- 8.8 Asymptotic Series as 0 for Solutions to Hyperbolic Problem -- 8.8.1 Estimates of Coefficients and Remaindersin (8.88), (8.89) -- 8.8.2 Estimate, Uniform with Respect to τ, of the Remainder ũN+1(·,τ,)in the Expansion (8.100) -- 8.8.3 Return to Non-extended Maxwell System (8.1) in (8.100), (8.101) -- 8.8.4 Complete Asymptotic Expansion of Solutions to Problem (8.111), (8.112) -- 8.9 Stationary Maxwell System with Impedance BoundaryConditions -- 8.10 Asymptotics for Solutions to Problem (8.192), (8.193) -- 8.10.1 Principal Term of Asymptotics -- 8.10.2 Estimate of the Remainder -- 8.10.3 Complete Asymptotic Expansion -- 8.10.4 Return to the Non-extended Maxwell System -- 8.11 Non-stationary Maxwell System with Impedance Boundary Conditions -- 8.12 Generalization to the Case of a Domain with Several SmallCavities -- Bibliographical Sketch -- References.
Record Nr. UNINA-9910483188003321
Korikov Dmitrii  
Cham, Switzerland : , : Birkhäuser, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Boundary integral equations / / George C. Hsiao, Wolfgang L. Wendland
Boundary integral equations / / George C. Hsiao, Wolfgang L. Wendland
Autore Hsiao G. C (George C.)
Edizione [Second edition.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (xx, 783 pages) : illustrations
Disciplina 620.00151535
Collana Applied mathematical sciences
Soggetto topico Boundary element methods
Integral equations
Problemes de contorn
Equacions integrals
Soggetto genere / forma Llibres electrònics
ISBN 3-030-71127-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface to the Second Edition -- Preface to the First Edition -- Acknowledgements -- Table of Contents -- 1. Introduction -- 1.1 The Green Representation Formula -- 1.2 Boundary Potentials and Calderón's Projector -- 1.3 Boundary Integral Equations -- 1.3.1 The Dirichlet Problem -- 1.3.2 The Neumann Problem -- 1.4 Exterior Problems -- 1.4.1 The Exterior Dirichlet Problem -- 1.4.2 The Exterior Neumann Problem -- 1.5 Remarks -- 2. Boundary Integral Equations -- 2.1 The Helmholtz Equation -- 2.1.1 Low Frequency Behaviour -- 2.2 The Lamé System -- 2.2.1 The Interior Displacement Problem -- 2.2.2 The Interior Traction Problem -- 2.2.3 Some Exterior Fundamental Problems -- 2.2.4 The Incompressible Material -- 2.3 The Stokes Equations -- 2.3.1 Hydrodynamic Potentials -- 2.3.2 The Stokes Boundary Value Problems -- 2.3.3 The Incompressible Material - Revisited -- 2.4 The Biharmonic Equation -- 2.4.1 Calderón's Projector -- 2.4.2 Boundary Value Problems and Boundary Integral Equations -- 2.5 Remarks -- 3. Representation Formulae, Local Coordinates and Direct Boundary Integral Equations -- 3.1 Classical Function Spaces and Distributions -- 3.2 Hadamard's Finite Part Integrals -- 3.3 Local Coordinates -- 3.4 Short Excursion to Elementary Differential Geometry -- 3.4.1 Second Order Differential Operators in Divergence Form -- 3.5 Distributional Derivatives and Abstract Green's Second Formula -- 3.6 The Green Representation Formula -- 3.7 Green's Representation Formulae in Local Coordinates -- 3.8 Multilayer Potentials -- 3.9 Direct Boundary Integral Equations -- 3.9.1 Boundary Value Problems -- 3.9.2 Transmission Problems -- 3.10 Remarks -- 4. Sobolev Spaces -- 4.1 The Spaces Hs(Ω) -- 4.2 The Trace Spaces Hs(Γ) -- 4.2.1 Trace Spaces for Periodic Functions on a Smooth Curve in IR -- 4.2.2 Trace Spaces on Curved Polygons in IR.
4.3 The Trace Spaces on an Open Surface -- 4.4 The Weighted Sobolev Spaces Hm(Ωc -- λ) and Hm(IRn -- λ) -- 4.5 Function Spaces H( div ,Ω) and H( curl,Ω) -- 5. Variational Formulations -- 5.1 Partial Differential Equations of Second Order -- 5.1.1 Interior Problems -- 5.1.2 Exterior Problems -- 5.1.3 Transmission Problems -- 5.2 Abstract Existence Theorems for Variational Problems -- 5.2.1 The Lax-Milgram Theorem -- 5.3 The Fredholm-Nikolski Theorems -- 5.3.1 Fredholm's Alternative -- 5.3.2 The Riesz-Schauder and the Nikolski Theorems -- 5.3.3 Fredholm's Alternative for Sesquilinear Forms -- 5.3.4 Fredholm Operators -- 5.4 Gårding's Inequality for Boundary Value Problems -- 5.4.1 Gårding's Inequality for Second Order Strongly Elliptic Equations in Ω -- 5.4.2 The Stokes System -- 5.4.3 Gårding's Inequality for Exterior Second Order Problems -- 5.4.4 Gårding's Inequality for Second Order Transmission Problems -- 5.5 Existence of Solutions to Strongly Elliptic Boundary Value Problems -- 5.5.1 Interior Boundary Value Problems -- 5.5.2 Exterior Boundary Value Problems -- 5.5.3 Transmission Problems -- 5.6 Solutions of Certain Boundary Integral Equations and Associated Boundary Value Problems -- 5.6.1 The Generalized Representation Formula for Second Order Systems -- 5.6.2 Continuity of Some Boundary Integral Operators -- 5.6.3 Continuity Based on Finite Regions -- 5.6.4 Continuity of Hydrodynamic Potentials -- 5.6.5 The Equivalence Between Boundary Value Problems and Integral Equations -- 5.6.6 Variational Formulation of Direct Boundary Integral Equations -- 5.6.7 Positivity and Contraction of Boundary Integral Operators -- 5.6.8 The Solvability of Direct Boundary Integral Equations -- 5.6.9 Positivity of the Boundary Integral Operators of the Stokes System -- 5.7 Partial Differential Equations of Higher Order -- 5.8 Remarks -- 5.8.1 Assumptions on Γ.
5.8.2 Higher Regularity of Solutions -- 5.8.3 Mixed Boundary Conditions and Crack Problem -- 6. Electromagnetic Fields -- 6.1 Introduction -- 6.2 Maxwell Equations -- 6.3 Constitutive Equations -- 6.4 Time Harmonic Fields -- 6.4.1 Plane waves -- 6.5 Electromagnetic potentials -- 6.6 Transmission and Boundary Conditions -- 6.7 Boundary Value Problems -- 6.7.1 Scattering problems -- 6.7.2 Eddy current problems -- 6.8 Uniqueness -- 6.8.1 The cavity problem -- 6.8.2 Exterior problems -- 6.8.3 The transmission problem -- 6.9 Representation Formulae -- 6.10 Boundary Integral Equations for Electromagnetic fields -- 6.10.1 The Calderon projector and the capacity operators -- 6.10.2 Weak solutions for a fundamental problem -- 6.10.2.1 Interior Dirichlet problem in Ω. -- 6.10.2.2 A reduction to boundary integral equations. -- 6.11 Application of the Electromagnetic Potentials to Eddy Current Problems -- 6.11.1 The '(A, ϕ) − (A) − (ψ)' formulation in the bounded domain -- 6.11.2 The '(A, ϕ) − (ψ)' formulation in an unbounded domain -- 6.11.3 Electric field in the dielectric domain ΩD. -- 6.11.4 Vector potentials - revisited -- 6.12 Applications of boundary integral equations to scattering problems -- 6.12.1 Scattering by a perfect electric conductor, EFIE and MFIE -- 6.12.2 Scattering by a dielectric body -- 6.12.3 Scattering by objects with impedance boundary conditions -- 7. Introduction to Pseudodifferential Operators -- 7.1 Basic Theory of Pseudodifferential Operators -- 7.2 Elliptic Pseudodifferential Operators on Ω ⊂ IRn -- 7.2.1 Systems of Pseudodifferential Operators -- 7.2.2 Parametrix and Fundamental Solution -- 7.2.3 Levi Functions for Scalar Elliptic Equations -- 7.2.4 Levi Functions for Elliptic Systems -- 7.2.5 Strong Ellipticity and Gårding's Inequality -- 7.3 Review on Fundamental Solutions -- 7.3.1 Local Fundamental Solutions.
7.3.2 Fundamental Solutions in IRn for Operators with Constant Coefficients -- 7.3.3 Existing Fundamental Solutions in Applications -- 8. Pseudodifferential Operators as Integral Operators -- 8.1 Pseudohomogeneous Kernels -- 8.1.1 Integral Operators as Pseudodifferential Operators of Negative Order -- 8.1.2 Non-Negative Order Pseudodifferential Operators as Hadamard Finite Part Integral Operators -- 8.1.3 Parity Conditions -- 8.1.4 A Summary of the Relations between Kernels and Symbols -- 8.2 Coordinate Changes and Pseudohomogeneous Kernels -- 8.2.1 The Transformation of General Hadamard Finite Part Integral Operators under Change of Coordinates -- 8.2.2 The Class of Invariant Hadamard Finite Part Integral Operators under Change of Coordinates -- 9. Pseudodifferential and Boundary Integral Operators -- 9.1 Pseudodifferential Operators on Boundary Manifolds -- 9.1.1 Ellipticity on Boundary Manifolds -- 9.1.2 Schwartz Kernels on Boundary Manifolds -- 9.2 Boundary Operators Generated by Domain Pseudodifferential Operators -- 9.3 Surface Potentials on the Plane IRn−1 -- 9.4 Pseudodifferential Operators with Symbols of Rational Type -- 9.5 Surface Potentials on the Boundary Manifold Γ -- 9.6 Volume Potentials -- 9.7 Strong Ellipticity and Fredholm Properties -- 9.8 Strong Ellipticity of Boundary Value Problems and Associated Boundary Integral Equations -- 9.8.1 The Boundary Value and Transmission Problems -- 9.8.2 The Associated Boundary Integral Equations of the First Kind -- 9.8.3 The Transmission Problem and Gårding's inequality -- 9.9 Remarks -- 10. Integral Equations on Γ ⊂ IR3 Recast as Pseudodifferential Equations -- 10.1 Newton Potential Operators for Elliptic Partial Differential Equations and Systems -- 10.1.1 Generalized Newton Potentials for the Helmholtz Equation -- 10.1.2 The Newton Potential for the Lamé System.
10.1.3 The Newton Potential for the Stokes System -- 10.2 Surface Potentials for Second Order Equations -- 10.2.1 Strongly Elliptic Differential Equations -- 10.2.2 Surface Potentials for the Helmholtz Equation -- 10.2.3 Surface Potentials for the Lamé System -- 10.2.4 Surface Potentials for the Stokes System -- 10.3 Invariance of Boundary Pseudodifferential Operators -- 10.3.1 The Hypersingular Boundary Integral Operators for the Helmholtz Equation -- 10.3.2 The Hypersingular Operator for the Lamé System -- 10.3.3 The Hypersingular Operator for the Stokes System -- 10.4 Derivatives of Boundary Potentials -- 10.4.1 Derivatives of the Solution to the Helmholtz Equation -- 10.4.2 Computation of Stress and Strain on the Boundary for the Lamé System -- 10.5 Remarks -- 11. Boundary Integral Equations on Curves in IR2 -- 11.1 Representation of the basic operators for the 2D-Laplacian in terms of Fourier series -- 11.2 The Fourier Series Representation of Periodic Operators A ∈ L m cl(Γ) -- 11.3 Ellipticity Conditions for Periodic Operators on Γ -- 11.3.1 Scalar Equations -- 11.3.2 Systems of Equations -- 11.3.3 Multiply Connected Domains -- 11.4 Fourier Series Representation of some Particular Operators -- 11.4.1 The Helmholtz Equation -- 11.4.2 The Lamé System -- 11.4.3 The Stokes System -- 11.4.4 The Biharmonic Equation -- 11.5 Remarks -- 12. Remarks on Pseudodifferential Operators Related to the Time Harmonic Maxwell Equations -- 12.1 Introduction -- 12.2 Symbols of P and the corresponding Newton potentials -- 12.3 Representation formulae -- 12.4 Symbols of the Electromagnetic Boundary Potentials -- 12.5 Symbols of boundary integral operators -- 12.6 Symbols of the Capacity Operators -- 12.7 Boundary Integral Operators for the Fundamental Boundary Value Problems -- 12.8 Coerciveness and Strong Ellipticity.
12.9 Gårding's inequality for the sesquilinear form A in (6.12.23).
Record Nr. UNISA-996466567503316
Hsiao G. C (George C.)  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Boundary integral equations / / George C. Hsiao, Wolfgang L. Wendland
Boundary integral equations / / George C. Hsiao, Wolfgang L. Wendland
Autore Hsiao G. C (George C.)
Edizione [Second edition.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (xx, 783 pages) : illustrations
Disciplina 620.00151535
Collana Applied mathematical sciences
Soggetto topico Boundary element methods
Integral equations
Problemes de contorn
Equacions integrals
Soggetto genere / forma Llibres electrònics
ISBN 3-030-71127-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface to the Second Edition -- Preface to the First Edition -- Acknowledgements -- Table of Contents -- 1. Introduction -- 1.1 The Green Representation Formula -- 1.2 Boundary Potentials and Calderón's Projector -- 1.3 Boundary Integral Equations -- 1.3.1 The Dirichlet Problem -- 1.3.2 The Neumann Problem -- 1.4 Exterior Problems -- 1.4.1 The Exterior Dirichlet Problem -- 1.4.2 The Exterior Neumann Problem -- 1.5 Remarks -- 2. Boundary Integral Equations -- 2.1 The Helmholtz Equation -- 2.1.1 Low Frequency Behaviour -- 2.2 The Lamé System -- 2.2.1 The Interior Displacement Problem -- 2.2.2 The Interior Traction Problem -- 2.2.3 Some Exterior Fundamental Problems -- 2.2.4 The Incompressible Material -- 2.3 The Stokes Equations -- 2.3.1 Hydrodynamic Potentials -- 2.3.2 The Stokes Boundary Value Problems -- 2.3.3 The Incompressible Material - Revisited -- 2.4 The Biharmonic Equation -- 2.4.1 Calderón's Projector -- 2.4.2 Boundary Value Problems and Boundary Integral Equations -- 2.5 Remarks -- 3. Representation Formulae, Local Coordinates and Direct Boundary Integral Equations -- 3.1 Classical Function Spaces and Distributions -- 3.2 Hadamard's Finite Part Integrals -- 3.3 Local Coordinates -- 3.4 Short Excursion to Elementary Differential Geometry -- 3.4.1 Second Order Differential Operators in Divergence Form -- 3.5 Distributional Derivatives and Abstract Green's Second Formula -- 3.6 The Green Representation Formula -- 3.7 Green's Representation Formulae in Local Coordinates -- 3.8 Multilayer Potentials -- 3.9 Direct Boundary Integral Equations -- 3.9.1 Boundary Value Problems -- 3.9.2 Transmission Problems -- 3.10 Remarks -- 4. Sobolev Spaces -- 4.1 The Spaces Hs(Ω) -- 4.2 The Trace Spaces Hs(Γ) -- 4.2.1 Trace Spaces for Periodic Functions on a Smooth Curve in IR -- 4.2.2 Trace Spaces on Curved Polygons in IR.
4.3 The Trace Spaces on an Open Surface -- 4.4 The Weighted Sobolev Spaces Hm(Ωc -- λ) and Hm(IRn -- λ) -- 4.5 Function Spaces H( div ,Ω) and H( curl,Ω) -- 5. Variational Formulations -- 5.1 Partial Differential Equations of Second Order -- 5.1.1 Interior Problems -- 5.1.2 Exterior Problems -- 5.1.3 Transmission Problems -- 5.2 Abstract Existence Theorems for Variational Problems -- 5.2.1 The Lax-Milgram Theorem -- 5.3 The Fredholm-Nikolski Theorems -- 5.3.1 Fredholm's Alternative -- 5.3.2 The Riesz-Schauder and the Nikolski Theorems -- 5.3.3 Fredholm's Alternative for Sesquilinear Forms -- 5.3.4 Fredholm Operators -- 5.4 Gårding's Inequality for Boundary Value Problems -- 5.4.1 Gårding's Inequality for Second Order Strongly Elliptic Equations in Ω -- 5.4.2 The Stokes System -- 5.4.3 Gårding's Inequality for Exterior Second Order Problems -- 5.4.4 Gårding's Inequality for Second Order Transmission Problems -- 5.5 Existence of Solutions to Strongly Elliptic Boundary Value Problems -- 5.5.1 Interior Boundary Value Problems -- 5.5.2 Exterior Boundary Value Problems -- 5.5.3 Transmission Problems -- 5.6 Solutions of Certain Boundary Integral Equations and Associated Boundary Value Problems -- 5.6.1 The Generalized Representation Formula for Second Order Systems -- 5.6.2 Continuity of Some Boundary Integral Operators -- 5.6.3 Continuity Based on Finite Regions -- 5.6.4 Continuity of Hydrodynamic Potentials -- 5.6.5 The Equivalence Between Boundary Value Problems and Integral Equations -- 5.6.6 Variational Formulation of Direct Boundary Integral Equations -- 5.6.7 Positivity and Contraction of Boundary Integral Operators -- 5.6.8 The Solvability of Direct Boundary Integral Equations -- 5.6.9 Positivity of the Boundary Integral Operators of the Stokes System -- 5.7 Partial Differential Equations of Higher Order -- 5.8 Remarks -- 5.8.1 Assumptions on Γ.
5.8.2 Higher Regularity of Solutions -- 5.8.3 Mixed Boundary Conditions and Crack Problem -- 6. Electromagnetic Fields -- 6.1 Introduction -- 6.2 Maxwell Equations -- 6.3 Constitutive Equations -- 6.4 Time Harmonic Fields -- 6.4.1 Plane waves -- 6.5 Electromagnetic potentials -- 6.6 Transmission and Boundary Conditions -- 6.7 Boundary Value Problems -- 6.7.1 Scattering problems -- 6.7.2 Eddy current problems -- 6.8 Uniqueness -- 6.8.1 The cavity problem -- 6.8.2 Exterior problems -- 6.8.3 The transmission problem -- 6.9 Representation Formulae -- 6.10 Boundary Integral Equations for Electromagnetic fields -- 6.10.1 The Calderon projector and the capacity operators -- 6.10.2 Weak solutions for a fundamental problem -- 6.10.2.1 Interior Dirichlet problem in Ω. -- 6.10.2.2 A reduction to boundary integral equations. -- 6.11 Application of the Electromagnetic Potentials to Eddy Current Problems -- 6.11.1 The '(A, ϕ) − (A) − (ψ)' formulation in the bounded domain -- 6.11.2 The '(A, ϕ) − (ψ)' formulation in an unbounded domain -- 6.11.3 Electric field in the dielectric domain ΩD. -- 6.11.4 Vector potentials - revisited -- 6.12 Applications of boundary integral equations to scattering problems -- 6.12.1 Scattering by a perfect electric conductor, EFIE and MFIE -- 6.12.2 Scattering by a dielectric body -- 6.12.3 Scattering by objects with impedance boundary conditions -- 7. Introduction to Pseudodifferential Operators -- 7.1 Basic Theory of Pseudodifferential Operators -- 7.2 Elliptic Pseudodifferential Operators on Ω ⊂ IRn -- 7.2.1 Systems of Pseudodifferential Operators -- 7.2.2 Parametrix and Fundamental Solution -- 7.2.3 Levi Functions for Scalar Elliptic Equations -- 7.2.4 Levi Functions for Elliptic Systems -- 7.2.5 Strong Ellipticity and Gårding's Inequality -- 7.3 Review on Fundamental Solutions -- 7.3.1 Local Fundamental Solutions.
7.3.2 Fundamental Solutions in IRn for Operators with Constant Coefficients -- 7.3.3 Existing Fundamental Solutions in Applications -- 8. Pseudodifferential Operators as Integral Operators -- 8.1 Pseudohomogeneous Kernels -- 8.1.1 Integral Operators as Pseudodifferential Operators of Negative Order -- 8.1.2 Non-Negative Order Pseudodifferential Operators as Hadamard Finite Part Integral Operators -- 8.1.3 Parity Conditions -- 8.1.4 A Summary of the Relations between Kernels and Symbols -- 8.2 Coordinate Changes and Pseudohomogeneous Kernels -- 8.2.1 The Transformation of General Hadamard Finite Part Integral Operators under Change of Coordinates -- 8.2.2 The Class of Invariant Hadamard Finite Part Integral Operators under Change of Coordinates -- 9. Pseudodifferential and Boundary Integral Operators -- 9.1 Pseudodifferential Operators on Boundary Manifolds -- 9.1.1 Ellipticity on Boundary Manifolds -- 9.1.2 Schwartz Kernels on Boundary Manifolds -- 9.2 Boundary Operators Generated by Domain Pseudodifferential Operators -- 9.3 Surface Potentials on the Plane IRn−1 -- 9.4 Pseudodifferential Operators with Symbols of Rational Type -- 9.5 Surface Potentials on the Boundary Manifold Γ -- 9.6 Volume Potentials -- 9.7 Strong Ellipticity and Fredholm Properties -- 9.8 Strong Ellipticity of Boundary Value Problems and Associated Boundary Integral Equations -- 9.8.1 The Boundary Value and Transmission Problems -- 9.8.2 The Associated Boundary Integral Equations of the First Kind -- 9.8.3 The Transmission Problem and Gårding's inequality -- 9.9 Remarks -- 10. Integral Equations on Γ ⊂ IR3 Recast as Pseudodifferential Equations -- 10.1 Newton Potential Operators for Elliptic Partial Differential Equations and Systems -- 10.1.1 Generalized Newton Potentials for the Helmholtz Equation -- 10.1.2 The Newton Potential for the Lamé System.
10.1.3 The Newton Potential for the Stokes System -- 10.2 Surface Potentials for Second Order Equations -- 10.2.1 Strongly Elliptic Differential Equations -- 10.2.2 Surface Potentials for the Helmholtz Equation -- 10.2.3 Surface Potentials for the Lamé System -- 10.2.4 Surface Potentials for the Stokes System -- 10.3 Invariance of Boundary Pseudodifferential Operators -- 10.3.1 The Hypersingular Boundary Integral Operators for the Helmholtz Equation -- 10.3.2 The Hypersingular Operator for the Lamé System -- 10.3.3 The Hypersingular Operator for the Stokes System -- 10.4 Derivatives of Boundary Potentials -- 10.4.1 Derivatives of the Solution to the Helmholtz Equation -- 10.4.2 Computation of Stress and Strain on the Boundary for the Lamé System -- 10.5 Remarks -- 11. Boundary Integral Equations on Curves in IR2 -- 11.1 Representation of the basic operators for the 2D-Laplacian in terms of Fourier series -- 11.2 The Fourier Series Representation of Periodic Operators A ∈ L m cl(Γ) -- 11.3 Ellipticity Conditions for Periodic Operators on Γ -- 11.3.1 Scalar Equations -- 11.3.2 Systems of Equations -- 11.3.3 Multiply Connected Domains -- 11.4 Fourier Series Representation of some Particular Operators -- 11.4.1 The Helmholtz Equation -- 11.4.2 The Lamé System -- 11.4.3 The Stokes System -- 11.4.4 The Biharmonic Equation -- 11.5 Remarks -- 12. Remarks on Pseudodifferential Operators Related to the Time Harmonic Maxwell Equations -- 12.1 Introduction -- 12.2 Symbols of P and the corresponding Newton potentials -- 12.3 Representation formulae -- 12.4 Symbols of the Electromagnetic Boundary Potentials -- 12.5 Symbols of boundary integral operators -- 12.6 Symbols of the Capacity Operators -- 12.7 Boundary Integral Operators for the Fundamental Boundary Value Problems -- 12.8 Coerciveness and Strong Ellipticity.
12.9 Gårding's inequality for the sesquilinear form A in (6.12.23).
Record Nr. UNINA-9910483092503321
Hsiao G. C (George C.)  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure / / by Pascal Auscher, Moritz Egert
Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure / / by Pascal Auscher, Moritz Egert
Autore Auscher Pascal
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023
Descrizione fisica 1 online resource (310 pages)
Disciplina 515.353
Altri autori (Persone) EgertMoritz
Collana Progress in Mathematics
Soggetto topico Differential equations
Harmonic analysis
Operator theory
Functional analysis
Differential Equations
Abstract Harmonic Analysis
Operator Theory
Functional Analysis
Equacions diferencials el·líptiques
Problemes de contorn
Espais de Hardy
Soggetto genere / forma Llibres electrònics
ISBN 3-031-29973-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter. 1. Introduction and main results -- Chapter. 2. Preliminaries on function spaces -- Chapter. 3. Preliminaries on operator theory -- Chapter. 4. Hp - Hq bounded families -- Chapter. 5. Conservation properties -- Chapter. 6. The four critical numbers -- Chapter. 7. Riesz transform estimates: Part I -- Chapter. 8. Operator-adapted spaces -- Chapter. 9. Identification of adapted Hardy spaces -- Chapter. 10. A digression: H -calculus and analyticity -- Chapter. 11. Riesz transform estimates: Part II -- Chapter. 12. Critical numbers for Poisson and heat semigroups -- Chapter. 13. Lp boundedness of the Hodge projector -- Chapter. 14. Critical numbers and kernel bounds -- Chapter. 15. Comparison with the Auscher–Stahlhut interval -- Chapter. 16. Basic properties of weak solutions -- Chapter. 17. Existence in Hp Dirichlet and Regularity problems -- Chapter. 18. Existence in the Dirichlet problems with data -- Chapter. 19. Existence in Dirichlet problems with fractional regularity data -- Chapter. 20. Single layer operators for L and estimates for L-1 -- Chapter. 21. Uniqueness in regularity and Dirichlet problems -- Chapter. 22. The Neumann problem -- Appendix A. Non-tangential maximal functions and traces -- Appendix B. The Lp-realization of a sectorial operator in L2 -- References -- Index.
Record Nr. UNINA-9910736007303321
Auscher Pascal  
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Convex integration applied to the multi-dimensional compressible Euler equations / / Simon Markfelder
Convex integration applied to the multi-dimensional compressible Euler equations / / Simon Markfelder
Autore Markfelder Simon
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (244 pages)
Disciplina 515.35
Collana Lecture Notes in Mathematics
Soggetto topico Differential equations
Physics
Global analysis (Mathematics)
Equacions de Lagrange
Funcions convexes
Integració numèrica
Problemes de contorn
Soggetto genere / forma Llibres electrònics
ISBN 3-030-83785-8
Classificazione 35Q31
76N10
35L65
35L45
35L50
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Part I The Problem Studied in This Book -- 1 Introduction -- 1.1 The Euler Equations -- 1.2 Weak Solutions and Admissibility -- 1.3 Overview on Well-Posedness Results -- 1.4 Structure of This Book -- 2 Hyperbolic Conservation Laws -- 2.1 Formulation of a Conservation Law -- 2.2 Initial Boundary Value Problem -- 2.3 Hyperbolicity -- 2.4 Companion Laws and Entropies -- 2.5 Admissible Weak Solutions -- 3 The Euler Equations as a Hyperbolic Systemof Conservation Laws -- 3.1 Barotropic Euler System -- 3.1.1 Hyperbolicity -- 3.1.2 Entropies -- 3.1.3 Admissible Weak Solutions -- 3.2 Full Euler System -- 3.2.1 Hyperbolicity -- 3.2.2 Entropies -- 3.2.3 Admissible Weak Solutions -- Part II Convex Integration -- 4 Preparation for Applying Convex Integrationto Compressible Euler -- 4.1 Outline and Preliminaries -- 4.1.1 Adjusting the Problem -- 4.1.2 Tartar's Framework -- 4.1.3 Plane Waves and the Wave Cone -- 4.1.4 Sketch of the Convex Integration Technique -- 4.2 -Convex Hulls -- 4.2.1 Definitions and Basic Facts -- 4.2.2 The HN-Condition and a Way to Define U -- 4.2.3 The -Convex Hull of Slices -- 4.2.4 The -Convex Hull if the Wave Cone is Complete -- 4.3 The Relaxed Set U Revisited -- 4.3.1 Definition of U -- 4.3.2 Computation of U -- 4.4 Operators -- 4.4.1 Statement of the Operators -- 4.4.2 Lemmas for the Proof of Proposition 4.4.1 -- 4.4.3 Proof of Proposition 4.4.1 -- 5 Implementation of Convex Integration -- 5.1 The Convex-Integration-Theorem -- 5.1.1 Statement of the Theorem -- 5.1.2 Functional Setup -- 5.1.3 The Functionals I0 and the Perturbation Property -- 5.1.4 Proof of the Convex-Integration-Theorem -- 5.2 Proof of the Perturbation Property -- 5.2.1 Lemmas for the Proof -- 5.2.2 Proof of Lemma 5.2.4 -- 5.2.3 Proof of Lemma 5.2.1 Using Lemmas 5.2.2, 5.2.3and 5.2.4.
5.2.4 Proof of the Perturbation Property Using Lemma 5.2.1 -- 5.3 Convex Integration with Fixed Density -- 5.3.1 A Modified Version of the Convex-Integration-Theorem -- 5.3.2 Proof the Modified Perturbation Property -- Part III Application to Particular Initial (Boundary) Value Problems -- 6 Infinitely Many Solutions of the Initial Boundary Value Problem for Barotropic Euler -- 6.1 A Simple Result on Weak Solutions -- 6.2 Possible Improvements to Obtain Admissible Weak Solutions -- 6.3 Further Possible Improvements -- 7 Riemann Initial Data in Two Space Dimensionsfor Isentropic Euler -- 7.1 One-Dimensional Self-Similar Solution -- 7.2 Summary of the Results on Non-/Uniqueness -- 7.3 Non-Uniqueness Proof if the Self-Similar Solution Consists of One Shock and One Rarefaction -- 7.3.1 Condition for Non-Uniqueness -- 7.3.2 The Corresponding System of Algebraic Equations and Inequalities -- 7.3.3 Simplification of the Algebraic System -- 7.3.4 Solution of the Algebraic System if the Rarefaction is ``Small'' -- 7.3.5 Proof of Theorem 7.3.1 via an Auxiliary State -- 7.4 Sketches of the Non-Uniqueness Proofs for the Other Cases -- 7.4.1 Two Shocks -- 7.4.2 One Shock -- 7.4.3 A Contact Discontinuity and at Least One Shock -- 7.5 Other Results in the Context of the Riemann Problem -- 8 Riemann Initial Data in Two Space Dimensions for Full Euler -- 8.1 One-Dimensional Self-Similar Solution -- 8.2 Summary of the Results on Non-/Uniqueness -- 8.3 Non-Uniqueness Proof if the Self-Similar Solution Contains Two Shocks -- 8.3.1 Condition for Non-Uniqueness -- 8.3.2 The Corresponding System of Algebraic Equations and Inequalities -- 8.3.3 Solution of the Algebraic System -- 8.4 Sketches of the Non-Uniqueness Proofs for the Other Cases -- 8.4.1 One Shock and One Rarefaction -- 8.4.2 One Shock -- 8.5 Other Results in the Context of the Riemann Problem.
A Notation and Lemmas -- A.1 Sets -- A.2 Vectors and Matrices -- A.2.1 General Euclidean Spaces -- A.2.2 The Physical Space and the Space-Time -- A.2.3 Phase Space -- A.3 Sequences -- A.4 Functions -- A.4.1 Basic Notions -- A.4.2 Differential Operators -- Functions of Time and Space -- Functions of the State Vector -- A.4.3 Function Spaces -- A.4.4 Integrability Conditions -- A.4.5 Boundary Integrals and the Divergence Theorem -- A.4.6 Mollifiers -- A.4.7 Periodic Functions -- A.5 Convexity -- A.5.1 Convex Sets and Convex Hulls -- A.5.2 Convex Functions -- A.6 Semi-Continuity -- A.7 Weak- Convergence in L∞ -- A.8 Baire Category Theorem -- Bibliography -- Index.
Record Nr. UNINA-9910506379703321
Markfelder Simon  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Convex integration applied to the multi-dimensional compressible Euler equations / / Simon Markfelder
Convex integration applied to the multi-dimensional compressible Euler equations / / Simon Markfelder
Autore Markfelder Simon
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (244 pages)
Disciplina 515.35
Collana Lecture Notes in Mathematics
Soggetto topico Differential equations
Physics
Global analysis (Mathematics)
Equacions de Lagrange
Funcions convexes
Integració numèrica
Problemes de contorn
Soggetto genere / forma Llibres electrònics
ISBN 3-030-83785-8
Classificazione 35Q31
76N10
35L65
35L45
35L50
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Part I The Problem Studied in This Book -- 1 Introduction -- 1.1 The Euler Equations -- 1.2 Weak Solutions and Admissibility -- 1.3 Overview on Well-Posedness Results -- 1.4 Structure of This Book -- 2 Hyperbolic Conservation Laws -- 2.1 Formulation of a Conservation Law -- 2.2 Initial Boundary Value Problem -- 2.3 Hyperbolicity -- 2.4 Companion Laws and Entropies -- 2.5 Admissible Weak Solutions -- 3 The Euler Equations as a Hyperbolic Systemof Conservation Laws -- 3.1 Barotropic Euler System -- 3.1.1 Hyperbolicity -- 3.1.2 Entropies -- 3.1.3 Admissible Weak Solutions -- 3.2 Full Euler System -- 3.2.1 Hyperbolicity -- 3.2.2 Entropies -- 3.2.3 Admissible Weak Solutions -- Part II Convex Integration -- 4 Preparation for Applying Convex Integrationto Compressible Euler -- 4.1 Outline and Preliminaries -- 4.1.1 Adjusting the Problem -- 4.1.2 Tartar's Framework -- 4.1.3 Plane Waves and the Wave Cone -- 4.1.4 Sketch of the Convex Integration Technique -- 4.2 -Convex Hulls -- 4.2.1 Definitions and Basic Facts -- 4.2.2 The HN-Condition and a Way to Define U -- 4.2.3 The -Convex Hull of Slices -- 4.2.4 The -Convex Hull if the Wave Cone is Complete -- 4.3 The Relaxed Set U Revisited -- 4.3.1 Definition of U -- 4.3.2 Computation of U -- 4.4 Operators -- 4.4.1 Statement of the Operators -- 4.4.2 Lemmas for the Proof of Proposition 4.4.1 -- 4.4.3 Proof of Proposition 4.4.1 -- 5 Implementation of Convex Integration -- 5.1 The Convex-Integration-Theorem -- 5.1.1 Statement of the Theorem -- 5.1.2 Functional Setup -- 5.1.3 The Functionals I0 and the Perturbation Property -- 5.1.4 Proof of the Convex-Integration-Theorem -- 5.2 Proof of the Perturbation Property -- 5.2.1 Lemmas for the Proof -- 5.2.2 Proof of Lemma 5.2.4 -- 5.2.3 Proof of Lemma 5.2.1 Using Lemmas 5.2.2, 5.2.3and 5.2.4.
5.2.4 Proof of the Perturbation Property Using Lemma 5.2.1 -- 5.3 Convex Integration with Fixed Density -- 5.3.1 A Modified Version of the Convex-Integration-Theorem -- 5.3.2 Proof the Modified Perturbation Property -- Part III Application to Particular Initial (Boundary) Value Problems -- 6 Infinitely Many Solutions of the Initial Boundary Value Problem for Barotropic Euler -- 6.1 A Simple Result on Weak Solutions -- 6.2 Possible Improvements to Obtain Admissible Weak Solutions -- 6.3 Further Possible Improvements -- 7 Riemann Initial Data in Two Space Dimensionsfor Isentropic Euler -- 7.1 One-Dimensional Self-Similar Solution -- 7.2 Summary of the Results on Non-/Uniqueness -- 7.3 Non-Uniqueness Proof if the Self-Similar Solution Consists of One Shock and One Rarefaction -- 7.3.1 Condition for Non-Uniqueness -- 7.3.2 The Corresponding System of Algebraic Equations and Inequalities -- 7.3.3 Simplification of the Algebraic System -- 7.3.4 Solution of the Algebraic System if the Rarefaction is ``Small'' -- 7.3.5 Proof of Theorem 7.3.1 via an Auxiliary State -- 7.4 Sketches of the Non-Uniqueness Proofs for the Other Cases -- 7.4.1 Two Shocks -- 7.4.2 One Shock -- 7.4.3 A Contact Discontinuity and at Least One Shock -- 7.5 Other Results in the Context of the Riemann Problem -- 8 Riemann Initial Data in Two Space Dimensions for Full Euler -- 8.1 One-Dimensional Self-Similar Solution -- 8.2 Summary of the Results on Non-/Uniqueness -- 8.3 Non-Uniqueness Proof if the Self-Similar Solution Contains Two Shocks -- 8.3.1 Condition for Non-Uniqueness -- 8.3.2 The Corresponding System of Algebraic Equations and Inequalities -- 8.3.3 Solution of the Algebraic System -- 8.4 Sketches of the Non-Uniqueness Proofs for the Other Cases -- 8.4.1 One Shock and One Rarefaction -- 8.4.2 One Shock -- 8.5 Other Results in the Context of the Riemann Problem.
A Notation and Lemmas -- A.1 Sets -- A.2 Vectors and Matrices -- A.2.1 General Euclidean Spaces -- A.2.2 The Physical Space and the Space-Time -- A.2.3 Phase Space -- A.3 Sequences -- A.4 Functions -- A.4.1 Basic Notions -- A.4.2 Differential Operators -- Functions of Time and Space -- Functions of the State Vector -- A.4.3 Function Spaces -- A.4.4 Integrability Conditions -- A.4.5 Boundary Integrals and the Divergence Theorem -- A.4.6 Mollifiers -- A.4.7 Periodic Functions -- A.5 Convexity -- A.5.1 Convex Sets and Convex Hulls -- A.5.2 Convex Functions -- A.6 Semi-Continuity -- A.7 Weak- Convergence in L∞ -- A.8 Baire Category Theorem -- Bibliography -- Index.
Record Nr. UNISA-996466386703316
Markfelder Simon  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Elliptic Carleman estimates and applications to stabilization and controllability . Volume II : general boundary conditions on Riemannian manifolds / / Jérôme Le Rousseau, Gilles Lebeau, and Luc Robbiano
Elliptic Carleman estimates and applications to stabilization and controllability . Volume II : general boundary conditions on Riemannian manifolds / / Jérôme Le Rousseau, Gilles Lebeau, and Luc Robbiano
Autore Le Rousseau Jérôme
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (542 pages)
Disciplina 512.73
Collana Progress in Nonlinear Differential Equations and Their Applications
Soggetto topico Riemannian manifolds
Boundary value problems
Varietats de Riemann
Problemes de contorn
Soggetto genere / forma Llibres electrònics
ISBN 3-030-88670-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996472038003316
Le Rousseau Jérôme  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui