Preface to the Second Printing. Preface to the First Printing Chapter 1 Generation and Representation 1.1 Uniformly Continuous Semigroups of Bounded Linear Operators 1.2 Strongly Continuous Semigroups of Bounded Linear Operators 1.3 The Hille-Yosida Theorem 1.4 The Lumer Phillips Theorem 1.5 The Characterization of the Infinitesimal Generators of Co Semigroups 1.6 Groups of Bounded Operators 1.7 The Inversion of the Laplace Transform 1.8 Two Exponential Formulas 1.9 Pseudo Resolvents 1.10 The Dual Semigroup Chapter 2 Spectral Properties and Regularity 2.1 Weak Equals Strong 2.2 Spectral Mapping Theorems 2.3 Semigroups of Compact Operators 2.4 Differentiability 2.5 Analytic Semigroups 2.6 Fractional Powers of Closed Operators Chapter 3 Perturbations and Approximations 3.1 Perturbations by Bounded Linear Operators 3.2 Perturbations of Infinitesimal Generators of Analytic Semigroups 3.3 Perturbations of Infinitesimal Generators of Contraction Semigroups 3.4 The Trotter Approximation Theorem 3.5 A General Representation Theorem 3.6 Approximation by Discrete Semigroups Chapter 4 The Abstract Cauchy Problem 4.1 The Homogeneous Initial Value Problem 4.2 The Inhomogeneous Initial Value Problem 4.3 Regularity of Mild Solutions for Analytic Semigroups 4.4 Asymptotic Behavior of Solutions 4.5 Invariant and Admissible Subspaces Chapter 5 Evolution Equations 5.1 Evolution Systems 5.2 Stable Families of Generators 5.3 An Evolution System in the Hyperbolic Case 5.4 Regular Solutions in the Hyperbolic Case 5.5 The Inhomogeneous Equation in the Hyperbolic Case 5.6 An Evolution System for the Parabolic Initial Value Problem 5.7 The Inhomogeneous Equation in the Parabolic Case 5.8 Asymptotic Behavior of Solutions in the Parabolic Case Chapter 6 Some Nonlinear Evolution Equations 6.1 Lipschitz Perturbations of Linear Evolution Equations 6.2 Semilinear Equations with Compact Semigroups 6.3 Semilinear Equations with Analytic Semigroups 6.4 A Quasilinear Equation of Evolution Chapter 7 Applications to Partial Differential Equations--Linear Equations 7.1 Introduction 7.2 Parabolic Equations--L2 Theory 7.3 Parabolic Equations--Lp Theory 7.4 The Wave Equation 7.5 A Sehr0dinger Equation 7.6 A Parabolic Evolution Equation Chapter 8 Applications to Partial Differential Equations--Nonlinear Equations 8.1 A Nonlinear Schrodinger Equation 8.2 A Nonlinear Heat Equation in R1 8.3 A Semilinear Evolution Equation in R3 8.4 A General Class of Semilinear Initial Value Problems 8.5 The Korteweg-de Vries Equation Bibliographical Notes and Remarks Bibliography Index
鄂公網(wǎng)安備 42010302001612號(hào) 