Systems with persistent memory : controllability, stability, identification / / Luciano Pandolfi

• Autore: Pandolfi L (Luciano)
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (365 pages)
• Disciplina: 511.8
• Soggetto topico: Mathematical models; Models matemàtics; Anàlisi funcional
• Soggetto genere / forma: Llibres electrònics
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Preliminary Considerations and Examples -- 1.1 The Systems with Persistent Memory Studied in This Book -- 1.2 Heuristics on the Wave and Heat Equations with and Without Memory -- 1.3 The Archetypal Model: The String Equation with Memory -- 1.3.1 The String Equation Without Memory on a Half Line -- 1.3.1.1 A Control Problem for the String Equation Without Memory -- 1.4 The String with Persistent Memory on a Half Line -- 1.4.1 Finite Propagation Speed -- 1.4.2 A Formula for the Solutions and a Control Problem -- 1.4.2.1 From the Regularity of the Input to the Interior Regularity -- 1.4.2.2 The Response Operator -- 1.4.2.3 From the Regularity of the Target to the Regularity of the Control -- 1.5 Diffusion Processes and Viscoelasticity: the Derivationof the Equations with Persistent Memory -- 1.5.1 Thermodynamics with Memory and Non-FickianDiffusion -- 1.5.2 Viscoelasticity -- 1.5.3 A Problem of Filtration -- 1.5.4 Physical Constraints -- References -- 2 Operators and Semigroups for Systems with Boundary Inputs -- 2.1 Preliminaries on Functional Analysis -- 2.1.1 Continuous Operators -- 2.1.2 The Complexification of Real Banach or Hilbert Spaces -- 2.1.3 Operators and Resolvents -- 2.1.4 Closed and Closable Operators -- 2.1.5 The Transpose and the Adjoint Operators -- 2.1.5.1 The Adjoint, the Transpose and the Imageof an Operator -- 2.1.6 Compact Operators in Hilbert Spaces -- 2.2 Integration, Volterra Integral Equations and Convolutions -- 2.3 Laplace Transformation -- 2.3.1 Holomorphic Functions in Banach Spaces -- 2.3.2 Definition and Properties of the Laplace Transformation -- 2.3.3 The Hardy Space H2(Π+ -- H ) and the LaplaceTransformation -- 2.4 Graph Norm, Dual Spaces, and the Riesz Map of Hilbert spaces -- 2.4.1 Relations of the Adjoint and the Transpose Operators. ; 2.5 Extension by Transposition and the Extrapolation Space -- 2.5.1 Selfadjoint Operators with Compact Resolvent -- 2.5.1.1 Fractional Powers of Positive Operatorswith Compact Resolvent -- 2.6 Distributions -- 2.6.1 Sobolev Spaces -- 2.6.1.1 Sobolev Spaces of Hilbert Space ValuedFunctions -- 2.6.1.2 Sobolev Spaces of Any Real Order -- 2.7 The Laplace Operator and the Laplace Equation -- 2.7.1 The Laplace Equation with Nonhomogeneous Dirichlet Boundary Conditions -- 2.7.2 The Laplace Equation with Nonhomogeneous Neumann Boundary Conditions -- 2.8 Semigroups of Operators -- 2.8.1 Holomorphic Semigroups -- 2.9 Cosine Operators and Differential Equations of the Second Order -- 2.10 Extensions by Transposition and Semigroups -- 2.10.1 Semigroups, Cosine Operators, and Boundary Inputs -- 2.11 On the Terminology and a Final Observation -- References -- 3 The Heat Equation with Memory and Its Controllability -- 3.1 The Abstract Heat Equation with Memory -- 3.2 Preliminaries on the Associated Memoryless System -- 3.2.1 Controllability of the Heat Equation (Without Memory) -- 3.3 Systems with Memory, Semigroups, and Volterra IntegralEquations -- 3.3.1 Projection on the Eigenfunctions -- 3.4 The Definitions of Controllability for the Heat Equationwith Memory -- 3.5 Memory Kernels of Class H1: Controllability via Semigroups -- 3.5.1 Approximate Controllability Is Inherited by the System with Memory -- 3.5.2 Controllability to the Target 0 Is Not Preserved -- 3.6 Frequency Domain Methods for Systems with Memory -- 3.6.1 Well Posedness via Laplace Transformation -- 3.7 Controllability via Laplace Transformation -- 3.7.1 Approximate Controllability Is Inherited by the System with Memory -- 3.7.2 Controllability to the Target 0 Is Not Preserved -- 3.8 Final Comments -- References -- 4 The Wave Equation with Memory and Its Controllability. ; 4.1 The Equations with and Without Memory -- 4.1.1 Admissibility and the Direct Inequality for the System Without Memory -- 4.2 The Solution of the Wave Equation with Memory -- 4.2.1 Admissibility and the Direct Inequality for the Wave Equation with Memory -- 4.2.1.1 Admissibility and Fourier Expansion -- 4.2.2 Finite Speed of Propagation -- 4.2.3 Memory Kernel of Class H2 and Compactness -- 4.3 The Definitions of Controllability and Their Consequences -- 4.3.1 Controllability of the Wave equation (Without Memory) with Dirichlet Boundary Controls -- 4.3.1.1 Fourier Expansions -- 4.3.2 Controllability of the Wave Equation (Without Memory) with Neumann Boundary Controls -- 4.3.2.1 Fourier Expansions -- 4.3.3 Controllability of the Wave Equation and Eigenvectors -- 4.4 Controllability of the Wave Equation with Memory:The Definitions -- 4.4.1 Computation of D,T* and N,T* -- 4.5 Wave Equation with Memory: the Proof of Controllability -- 4.6 Final Comments -- References -- 5 The Stability of the Wave Equation with Persistent Memory -- 5.1 Introduction to Stability -- 5.2 The Memory Kernel When the System Is Stable -- 5.2.1 Consequent Properties of the Memory Kernel M(t) -- 5.2.1.1 The Real and the Imaginary Parts of (λ) -- 5.2.1.2 The Resolvent Kernel R(t) of -M(t) -- 5.2.2 Positive Real (Transfer) Functions -- 5.3 L2-Stability via Laplace Transform and Frequency Domain Techniques -- 5.3.1 L2-Stability When =0 -- 5.3.2 The Memory Prior to the Time 0 -- 5.4 Stability via Energy Estimates -- 5.5 Stability via the Semigroup Approach of Dafermos -- 5.5.1 Generation of the Semigroup in the History Space -- 5.5.2 Exponential Stability via Semigroups -- 5.6 Final Comments -- References -- 6 Dynamical Algorithms for Identification Problems -- 6.1 Introduction to Identification Problems -- 6.1.1 Deconvolution and Numerical Computationof Derivatives. ; 6.2 Dynamical Algorithms for Kernel Identification -- 6.2.1 A Linear Algorithm with Two Independent Measurements: Reduction to a Deconvolution Problem -- 6.2.2 One Measurement: A Nonlinear Identification Algorithm -- 6.2.3 Quasi Static Algorithms -- 6.3 Dynamical Identification of an Elastic Coefficient -- 6.3.1 From the Connecting Operator to the Identification of q(x) -- 6.3.2 The Blagoveshchenskiǐ Equation and the Computationof the Connecting Operator -- 6.3.2.1 Well Posedness of the Blagoveshchenskiǐ Equation -- 6.4 Final Comments -- References -- 7 Final Miscellaneous Problems -- 7.1 Solutions of a Nonlinear System with Memory: Galerkin's Method -- 7.2 Asymptotics of Linear Heat Equations with Memory Perturbed by a Sector Nonlinearity -- 7.2.1 Dafermos Method for the Heat Equation with Memory -- 7.2.2 Asymptotic Properties of the Perturbed Equation -- 7.3 Controllability and Small Perturbations -- 7.3.1 The Belleni-Morante Method and Controllability -- 7.4 Memory on the Boundary -- 7.5 A Glimpse to Numerical Methods for Systems with Persistent Memory -- References -- Index.
• Titolo autorizzato: Systems with Persistent Memory
• ISBN: 3-030-80281-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466399703316
• Lo trovi qui: Univ. di Salerno
• Serie: Interdisciplinary applied mathematics ; ; 54.