线性算子半单群及其在偏微分方程中的应用(英文版)

本书是一部关于线性算子半群理论及其在偏微分方程中应用的经典教科书，内容简明，书中着重介绍用于偏微分方程的实初始值问题，以及自治和非自治线性初始值问题用的抽象柯西问题。适用于数学及相关专业研究生。

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