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线性算子半单群及其在偏微分方程中的应用2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

线性算子半单群及其在偏微分方程中的应用
  • （美）A. Pazy 著
  • 出版社： 世界图书出版公司北京公司
  • ISBN：7506282275
  • 出版时间：2006
  • 标注页数：281页
  • 文件大小：48MB
  • 文件页数：291页
  • 主题词：线性算子半群－应用－偏微分方程－高等学校－教材－英文

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图书目录

Chapter 1 Generation and Representation1

1.1 Uniformly Continuous Semigroups of Bounded Linear Operators1

1.2 Strongly Continuous Semigroups of Bounded Linear Operators4

1.3 The Hille-Yosida Theorem8

1.4 The Lumer Phillips Theorem13

1.5 The Characterization of the Infinitesimal Generators of C0 Semigroups17

1.6 Groups of Bounded Operators22

1.7 The Inversion of the Laplace Transform25

1.8 Two Exponential Formulas32

1.9 Pseudo Resolvents36

1.10 The Dual Semigroup38

Chapter 2 Spectral Properties and Regularity42

2.1 Weak Equals Strong42

2.2 Spectral Mapping Theorems44

2.3 Semigroups of Compact Operators48

2.4 Differentiability51

2.5 Analytic Semigroups60

2.6 Fractional Powers of Closed Operators69

Chapter 3 Perturbations and Approximations76

3.1 Perturbations by Bounded Linear Operators76

3.2 Perturbations of Infinitesimal Generators of Analytic Semigroups80

3.3 Perturbations of Infinitesimal Generators of Contraction Semigroups81

3.4 The Trotter Approximation Theorem84

3.5 A General Representation Theorem89

3.6 Approximation by Discrete Semigroups94

Chapter 4 The Abstract Cauchy Problem100

4.1 The Homogeneous Initial Value Problem100

4.2 The Inhomogeneous Initial Value Problem105

4.3 Regularity of Mild Solutions for Analytic Semigroups110

4.4 Asymptotic Behavior of Solutions115

4.5 Invariant and Admissible Subspaces121

Chapter 5 Evolution Equations126

5.1 Evolution Systems126

5.2 Stable Families of Generators130

5.3 An Evolution System in the Hyperbolic Case134

5.4 Regular Solutions in the Hyperbolic Case139

5.5 The Inhomogeneous Equation in the Hyperbolic Case146

5.6 An Evolution System for the Parabolic Initial Value Problem149

5.7 The Inhomogeneous Equation in the Parabolic Case167

5.8 Asymptotic Behavior of Solutions in the Parabolic Case172

Chapter 6 Some Nonlinear Evolution Equations183

6.1 Lipschitz Perturbations of Linear Evolution Equations183

6.2 Semilinear Equations with Compact Semigroups191

6.3 Semilinear Equations with Analytic Semigroups195

6.4 A Quasilinear Equation of Evolution200

Chapter 7 Applications to Partial Differential Equations—Linear Equations206

7.1 Introduction206

7.2 Parabolic Equations—L2 Theory208

7.3 Parabolic Equations—Lp Theory212

7.4 The Wave Equation219

7.5 A Schr？dinger Equation223

7.6 A Parabolic Evolution Equation225

Chapter 8 Applications to Partial Differential Equations—Nonlinear Equations230

8.1 A Nonlinear Schr？dinger Equation230

8.2 A Nonlinear Heat Equation in R1234

8.3 A Semilinear Evolution Equation in R3238

8.4 A General Class of Semilinear Initial Value Problems241

8.5 The Korteweg-de Vries Equation247

Bibliographical Notes and Remarks252

Bibliography264

Index277

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