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Asymptotic models of fields in dilute and densely packed composites [[electronic resource] /] / A.B. Movchan, N.V. Movchan, C.G. Poulton
Asymptotic models of fields in dilute and densely packed composites [[electronic resource] /] / A.B. Movchan, N.V. Movchan, C.G. Poulton
Autore Movchan A. B (Alexander B.)
Pubbl/distr/stampa London, : Imperial College Press
Descrizione fisica 1 online resource (204 p.)
Disciplina 620.118
Altri autori (Persone) MovchanN. V (Nataliya V.)
PoultonC. G (Chris G.)
Soggetto topico Boundary value problems - Asymptotic theory
Composite materials - Defects - Mathematical models
Differential equations, Partial - Asymptotic theory
Elasticity
Electromagnetism
Soggetto genere / forma Electronic books.
ISBN 1-86094-961-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents ; Preface ; Chapter 1 Long and close range interaction within elastic structures ; 1.1 Dilute composite structures. Scalar problems ; 1.1.1 An elementary example. Motivation ; 1.1.2 Asymptotic algorithm involving a boundary layer ; 1.1.2.1 Formulation of the problem
1.1.2.2 The leading-order approximation 1.1.2.3 Asymptotic formula for the energy ; 1.1.3 The dipole matrix ; 1.1.3.1 Definition of the dipole matrix ; 1.1.3.2 Symmetry of the dipole matrix ; 1.1.3.3 The energy asymptotics for a body with a small void
1.1.4 Dipole matrix for a 2D void in an infinite plane 1.1.5 Dipole matrices for inclusions ; 1.1.6 A note on homogenization of dilute periodic structures ; 1.2 Dipole fields in vector problems of linear elasticity ; 1.2.1 Definitions and governing equations
1.2.2 Physical interpretation 1.2.3 Evaluation of the elements of the dipole matrix ; 1.2.4 Examples ; 1.2.5 The energy equivalent voids ; 1.3 Circular elastic inclusions ; 1.3.1 Inclusions with perfect bonding at the interface ; 1.3.2 Dipole tensors for imperfectly bonded inclusions
1.3.2.1 Derivation of transmission conditions at the zero-thickness interface 1.3.2.2 Neutral coated inclusions ; 1.4 Close-range contact between elastic inclusions ; 1.4.1 Governing equations ; 1.4.2 Complex potentials ; 1.4.3 Analysis for two circular elastic inclusions
1.4.4 Square array of circular inclusions
Record Nr. UNINA-9910457965003321
Movchan A. B (Alexander B.)  
London, : Imperial College Press
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic models of fields in dilute and densely packed composites [[electronic resource] /] / A.B. Movchan, N.V. Movchan, C.G. Poulton
Asymptotic models of fields in dilute and densely packed composites [[electronic resource] /] / A.B. Movchan, N.V. Movchan, C.G. Poulton
Autore Movchan A. B (Alexander B.)
Pubbl/distr/stampa London, : Imperial College Press
Descrizione fisica 1 online resource (204 p.)
Disciplina 620.118
Altri autori (Persone) MovchanN. V (Nataliya V.)
PoultonC. G (Chris G.)
Soggetto topico Boundary value problems - Asymptotic theory
Composite materials - Defects - Mathematical models
Differential equations, Partial - Asymptotic theory
Elasticity
Electromagnetism
ISBN 1-86094-961-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents ; Preface ; Chapter 1 Long and close range interaction within elastic structures ; 1.1 Dilute composite structures. Scalar problems ; 1.1.1 An elementary example. Motivation ; 1.1.2 Asymptotic algorithm involving a boundary layer ; 1.1.2.1 Formulation of the problem
1.1.2.2 The leading-order approximation 1.1.2.3 Asymptotic formula for the energy ; 1.1.3 The dipole matrix ; 1.1.3.1 Definition of the dipole matrix ; 1.1.3.2 Symmetry of the dipole matrix ; 1.1.3.3 The energy asymptotics for a body with a small void
1.1.4 Dipole matrix for a 2D void in an infinite plane 1.1.5 Dipole matrices for inclusions ; 1.1.6 A note on homogenization of dilute periodic structures ; 1.2 Dipole fields in vector problems of linear elasticity ; 1.2.1 Definitions and governing equations
1.2.2 Physical interpretation 1.2.3 Evaluation of the elements of the dipole matrix ; 1.2.4 Examples ; 1.2.5 The energy equivalent voids ; 1.3 Circular elastic inclusions ; 1.3.1 Inclusions with perfect bonding at the interface ; 1.3.2 Dipole tensors for imperfectly bonded inclusions
1.3.2.1 Derivation of transmission conditions at the zero-thickness interface 1.3.2.2 Neutral coated inclusions ; 1.4 Close-range contact between elastic inclusions ; 1.4.1 Governing equations ; 1.4.2 Complex potentials ; 1.4.3 Analysis for two circular elastic inclusions
1.4.4 Square array of circular inclusions
Record Nr. UNINA-9910784798703321
Movchan A. B (Alexander B.)  
London, : Imperial College Press
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic models of fields in dilute and densely packed composites / / A.B. Movchan, N.V. Movchan, C.G. Poulton
Asymptotic models of fields in dilute and densely packed composites / / A.B. Movchan, N.V. Movchan, C.G. Poulton
Autore Movchan A. B (Alexander B.)
Edizione [1st ed.]
Pubbl/distr/stampa London, : Imperial College Press
Descrizione fisica 1 online resource (204 p.)
Disciplina 620.118
Altri autori (Persone) MovchanN. V (Nataliya V.)
PoultonC. G (Chris G.)
Soggetto topico Boundary value problems - Asymptotic theory
Composite materials - Defects - Mathematical models
Differential equations, Partial - Asymptotic theory
Elasticity
Electromagnetism
ISBN 1-86094-961-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents ; Preface ; Chapter 1 Long and close range interaction within elastic structures ; 1.1 Dilute composite structures. Scalar problems ; 1.1.1 An elementary example. Motivation ; 1.1.2 Asymptotic algorithm involving a boundary layer ; 1.1.2.1 Formulation of the problem
1.1.2.2 The leading-order approximation 1.1.2.3 Asymptotic formula for the energy ; 1.1.3 The dipole matrix ; 1.1.3.1 Definition of the dipole matrix ; 1.1.3.2 Symmetry of the dipole matrix ; 1.1.3.3 The energy asymptotics for a body with a small void
1.1.4 Dipole matrix for a 2D void in an infinite plane 1.1.5 Dipole matrices for inclusions ; 1.1.6 A note on homogenization of dilute periodic structures ; 1.2 Dipole fields in vector problems of linear elasticity ; 1.2.1 Definitions and governing equations
1.2.2 Physical interpretation 1.2.3 Evaluation of the elements of the dipole matrix ; 1.2.4 Examples ; 1.2.5 The energy equivalent voids ; 1.3 Circular elastic inclusions ; 1.3.1 Inclusions with perfect bonding at the interface ; 1.3.2 Dipole tensors for imperfectly bonded inclusions
1.3.2.1 Derivation of transmission conditions at the zero-thickness interface 1.3.2.2 Neutral coated inclusions ; 1.4 Close-range contact between elastic inclusions ; 1.4.1 Governing equations ; 1.4.2 Complex potentials ; 1.4.3 Analysis for two circular elastic inclusions
1.4.4 Square array of circular inclusions
Record Nr. UNINA-9910816450503321
Movchan A. B (Alexander B.)  
London, : Imperial College Press
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
Asymptotic theory of elliptic boundary value problems in singularly perturbed domains / Vladimir Maz'ya, Serguei Nazarov, Boris Plamenevskij ; translated from the German by Georg Heinig and Christian Posthoff
Asymptotic theory of elliptic boundary value problems in singularly perturbed domains / Vladimir Maz'ya, Serguei Nazarov, Boris Plamenevskij ; translated from the German by Georg Heinig and Christian Posthoff
Autore Maz'ya, Vladimir G.
Pubbl/distr/stampa Basel ; Boston ; Berlin : Birkhäuser Verlag, c2000
Descrizione fisica 2 v. : ill. ; 24 cm
Disciplina 515.353
Altri autori (Persone) Nazarov, Serguei A.
Plamenevskiæi, Boris A.
Collana OOperator theory. Advances and applications ; 111-112
Soggetto topico Boundary value problems - Asymptotic theory
Differential equations, Elliptic - Asymptotic theory
Perturbation (Mathematics)
Singularities (Mathematics)
ISBN 3764329645 (set)
3764363975 (v. 1)
3764363983 (v. 2)
Classificazione AMS 35J25
AMS 35B25
AMS 73B27
AMS 35B40
AMS 73C02
AMS 35J40
LC QA379.M3913
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Titolo uniforme
Record Nr. UNISALENTO-991001416839707536
Maz'ya, Vladimir G.  
Basel ; Boston ; Berlin : Birkhäuser Verlag, c2000
Materiale a stampa
Lo trovi qui: Univ. del Salento
Opac: Controlla la disponibilità qui
Canard cycles and center manifolds / / Freddy Dumortier, Robert Roussarie
Canard cycles and center manifolds / / Freddy Dumortier, Robert Roussarie
Autore Dumortier Freddy
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 1996
Descrizione fisica 1 online resource (117 p.)
Disciplina 515/.352
Collana Memoirs of the American Mathematical Society
Soggetto topico Boundary value problems - Asymptotic theory
Perturbation (Mathematics)
Bifurcation theory
Soggetto genere / forma Electronic books.
ISBN 1-4704-0162-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""3 Foliations by center manifolds""""3.1 Normal forms for X at the non-isolated singular points""; ""3.2 Construction of center manifolds""; ""3.2.1 Center manifolds of type I""; ""3.2.2 Center manifolds of type II""; ""3.2.3 Center manifolds of type III""; ""3.2.4 Pictures of the center manifolds""; ""3.3 Foliations by center manifolds""; ""3.3.1 Foliation of type I""; ""3.3.2 Foliation of type II""; ""3.3.3 Foliations of type III""; ""4 The canard phenomenon""; ""4.1 The small limit periodic set""; ""4.2 Relation between the Abelian integrals and the center manifolds""
""4.3 Explanation of the canard phenomenon by means of center manifolds""""4.3.1 Canard limit periodic sets of type I""; ""4.3.2 Canard limit periodic sets of type III""; ""4.3.3 Canard limit periodic sets of type II""; ""4.3.4 Bringing the foliations together (as a final step)""; ""References""; ""Appendix: on the proof of theorem 18""
Record Nr. UNINA-9910480683703321
Dumortier Freddy  
Providence, Rhode Island : , : American Mathematical Society, , 1996
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Canard cycles and center manifolds / / Freddy Dumortier, Robert Roussarie
Canard cycles and center manifolds / / Freddy Dumortier, Robert Roussarie
Autore Dumortier Freddy
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 1996
Descrizione fisica 1 online resource (117 p.)
Disciplina 515/.352
Collana Memoirs of the American Mathematical Society
Soggetto topico Boundary value problems - Asymptotic theory
Perturbation (Mathematics)
Bifurcation theory
ISBN 1-4704-0162-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""3 Foliations by center manifolds""""3.1 Normal forms for X at the non-isolated singular points""; ""3.2 Construction of center manifolds""; ""3.2.1 Center manifolds of type I""; ""3.2.2 Center manifolds of type II""; ""3.2.3 Center manifolds of type III""; ""3.2.4 Pictures of the center manifolds""; ""3.3 Foliations by center manifolds""; ""3.3.1 Foliation of type I""; ""3.3.2 Foliation of type II""; ""3.3.3 Foliations of type III""; ""4 The canard phenomenon""; ""4.1 The small limit periodic set""; ""4.2 Relation between the Abelian integrals and the center manifolds""
""4.3 Explanation of the canard phenomenon by means of center manifolds""""4.3.1 Canard limit periodic sets of type I""; ""4.3.2 Canard limit periodic sets of type III""; ""4.3.3 Canard limit periodic sets of type II""; ""4.3.4 Bringing the foliations together (as a final step)""; ""References""; ""Appendix: on the proof of theorem 18""
Record Nr. UNINA-9910788760003321
Dumortier Freddy  
Providence, Rhode Island : , : American Mathematical Society, , 1996
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Canard cycles and center manifolds / / Freddy Dumortier, Robert Roussarie
Canard cycles and center manifolds / / Freddy Dumortier, Robert Roussarie
Autore Dumortier Freddy
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 1996
Descrizione fisica 1 online resource (117 p.)
Disciplina 515/.352
Collana Memoirs of the American Mathematical Society
Soggetto topico Boundary value problems - Asymptotic theory
Perturbation (Mathematics)
Bifurcation theory
ISBN 1-4704-0162-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""3 Foliations by center manifolds""""3.1 Normal forms for X at the non-isolated singular points""; ""3.2 Construction of center manifolds""; ""3.2.1 Center manifolds of type I""; ""3.2.2 Center manifolds of type II""; ""3.2.3 Center manifolds of type III""; ""3.2.4 Pictures of the center manifolds""; ""3.3 Foliations by center manifolds""; ""3.3.1 Foliation of type I""; ""3.3.2 Foliation of type II""; ""3.3.3 Foliations of type III""; ""4 The canard phenomenon""; ""4.1 The small limit periodic set""; ""4.2 Relation between the Abelian integrals and the center manifolds""
""4.3 Explanation of the canard phenomenon by means of center manifolds""""4.3.1 Canard limit periodic sets of type I""; ""4.3.2 Canard limit periodic sets of type III""; ""4.3.3 Canard limit periodic sets of type II""; ""4.3.4 Bringing the foliations together (as a final step)""; ""References""; ""Appendix: on the proof of theorem 18""
Record Nr. UNINA-9910829054703321
Dumortier Freddy  
Providence, Rhode Island : , : American Mathematical Society, , 1996
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Free boundary problems and asymptotic behavior of singularly perturbed partial differential equations / / Kelei Wang
Free boundary problems and asymptotic behavior of singularly perturbed partial differential equations / / Kelei Wang
Autore Wang Kelei
Edizione [1st ed. 2013.]
Pubbl/distr/stampa Berlin ; ; Heidelberg, : Springer, c2013
Descrizione fisica 1 online resource (116 p.)
Disciplina 515.353
Collana Springer theses
Soggetto topico Boundary value problems - Asymptotic theory
Differential equations, Partial - Asymptotic theory
ISBN 1-283-91080-2
3-642-33696-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Foreword -- Acknowledgements -- Introduction -- Uniqueness, Stability and Uniform Lipschitz Estimates -- Uniqueness in the Singular Limit -- The Dynamics of One Dimensional Singular Limiting Problem.- Approximate Clean Up Lemma.- Asymptotics in Strong Competition -- The Limited Equation of a Singular Perturbed System -- Reference -- Index.
Record Nr. UNINA-9910438146003321
Wang Kelei  
Berlin ; ; Heidelberg, : Springer, c2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui