Banach空间中的单调算子与非线性偏微分方程（影印版）
定价：￥135.00
作者： R.E.Showalter
出版社：高等教育出版社
- 高等教育出版社
- 9787040661347
- 1版
- 64270575-0
- 特殊
- 理学
- 数学类
- 数学类
- 本科 研究生及以上
目录
目录
前辅文
Preface
PDE Examples by Type
Chapter I. Linear Problems ... an Introduction
I.1 Boundary-Value Problems in 1-D
I.2 Variational Method in Hilbert Space
I.3 Applications to Stretched String Problems
I.4 Unbounded Operators
I.5 The Cauchy Problem
I.6 Wave Equations
Chapter II. Nonlinear Stationary Problems
II.1 Banach Spaces
II.2 Existence Theorems
II.3 LP Spaces
II.4 Sobolev Spaces
II.5 Elliptic Boundary-Value Problems
II.6 Variational Inequalities and Quasimonotone Operators
II.7 Convex Functions
II.8 Examples
II.9 Elliptic Equations in L1
Chapter III. Nonlinear Evolution Problems
III.1 Vector-valued Functions
III.2 Linear Evolution Equations
III.3 Linear Degenerate Equations
III.4 Nonlinear Parabolic Equations
III.5 Abstract Difference Approximations
III.6 Degenerate Parabolic Equations
III.7 Variational Inequalities
Chapter IV. Accretive Operators and Nonlinear Cauchy Problems
IV.1 Accretive Operators in Hilbert Space
IV.2 Examples of m-accretive Operators
IV.3 The Cauchy Problem in Hilbert Space
IV.4 Additional Topics and Evolution Equations
IV.5 Parabolic Equations and Inequalities
IV.6 Semilinear Degenerate Evolution Equations
IV.7 Accretive Operators in Banach Space
IV.8 The Cauchy Problem in General Banach Space
IV.9 Evolution Equations in L1
Appendix: Applications
A.1 Heat Conduction
A.2 Flow in Porous Media
A.3 Continuum Mechanics
Bibliography
Index
前辅文
Preface
PDE Examples by Type
Chapter I. Linear Problems ... an Introduction
I.1 Boundary-Value Problems in 1-D
I.2 Variational Method in Hilbert Space
I.3 Applications to Stretched String Problems
I.4 Unbounded Operators
I.5 The Cauchy Problem
I.6 Wave Equations
Chapter II. Nonlinear Stationary Problems
II.1 Banach Spaces
II.2 Existence Theorems
II.3 LP Spaces
II.4 Sobolev Spaces
II.5 Elliptic Boundary-Value Problems
II.6 Variational Inequalities and Quasimonotone Operators
II.7 Convex Functions
II.8 Examples
II.9 Elliptic Equations in L1
Chapter III. Nonlinear Evolution Problems
III.1 Vector-valued Functions
III.2 Linear Evolution Equations
III.3 Linear Degenerate Equations
III.4 Nonlinear Parabolic Equations
III.5 Abstract Difference Approximations
III.6 Degenerate Parabolic Equations
III.7 Variational Inequalities
Chapter IV. Accretive Operators and Nonlinear Cauchy Problems
IV.1 Accretive Operators in Hilbert Space
IV.2 Examples of m-accretive Operators
IV.3 The Cauchy Problem in Hilbert Space
IV.4 Additional Topics and Evolution Equations
IV.5 Parabolic Equations and Inequalities
IV.6 Semilinear Degenerate Evolution Equations
IV.7 Accretive Operators in Banach Space
IV.8 The Cauchy Problem in General Banach Space
IV.9 Evolution Equations in L1
Appendix: Applications
A.1 Heat Conduction
A.2 Flow in Porous Media
A.3 Continuum Mechanics
Bibliography
Index
前辅文
Preface
PDE Examples by Type
Chapter I. Linear Problems ... an Introduction
I.1 Boundary-Value Problems in 1-D
I.2 Variational Method in Hilbert Space
I.3 Applications to Stretched String Problems
I.4 Unbounded Operators
I.5 The Cauchy Problem
I.6 Wave Equations
Chapter II. Nonlinear Stationary Problems
II.1 Banach Spaces
II.2 Existence Theorems
II.3 LP Spaces
II.4 Sobolev Spaces
II.5 Elliptic Boundary-Value Problems
II.6 Variational Inequalities and Quasimonotone Operators
II.7 Convex Functions
II.8 Examples
II.9 Elliptic Equations in L1
Chapter III. Nonlinear Evolution Problems
III.1 Vector-valued Functions
III.2 Linear Evolution Equations
III.3 Linear Degenerate Equations
III.4 Nonlinear Parabolic Equations
III.5 Abstract Difference Approximations
III.6 Degenerate Parabolic Equations
III.7 Variational Inequalities
Chapter IV. Accretive Operators and Nonlinear Cauchy Problems
IV.1 Accretive Operators in Hilbert Space
IV.2 Examples of m-accretive Operators
IV.3 The Cauchy Problem in Hilbert Space
IV.4 Additional Topics and Evolution Equations
IV.5 Parabolic Equations and Inequalities
IV.6 Semilinear Degenerate Evolution Equations
IV.7 Accretive Operators in Banach Space
IV.8 The Cauchy Problem in General Banach Space
IV.9 Evolution Equations in L1
Appendix: Applications
A.1 Heat Conduction
A.2 Flow in Porous Media
A.3 Continuum Mechanics
Bibliography
Index
前辅文
Preface
PDE Examples by Type
Chapter I. Linear Problems ... an Introduction
I.1 Boundary-Value Problems in 1-D
I.2 Variational Method in Hilbert Space
I.3 Applications to Stretched String Problems
I.4 Unbounded Operators
I.5 The Cauchy Problem
I.6 Wave Equations
Chapter II. Nonlinear Stationary Problems
II.1 Banach Spaces
II.2 Existence Theorems
II.3 LP Spaces
II.4 Sobolev Spaces
II.5 Elliptic Boundary-Value Problems
II.6 Variational Inequalities and Quasimonotone Operators
II.7 Convex Functions
II.8 Examples
II.9 Elliptic Equations in L1
Chapter III. Nonlinear Evolution Problems
III.1 Vector-valued Functions
III.2 Linear Evolution Equations
III.3 Linear Degenerate Equations
III.4 Nonlinear Parabolic Equations
III.5 Abstract Difference Approximations
III.6 Degenerate Parabolic Equations
III.7 Variational Inequalities
Chapter IV. Accretive Operators and Nonlinear Cauchy Problems
IV.1 Accretive Operators in Hilbert Space
IV.2 Examples of m-accretive Operators
IV.3 The Cauchy Problem in Hilbert Space
IV.4 Additional Topics and Evolution Equations
IV.5 Parabolic Equations and Inequalities
IV.6 Semilinear Degenerate Evolution Equations
IV.7 Accretive Operators in Banach Space
IV.8 The Cauchy Problem in General Banach Space
IV.9 Evolution Equations in L1
Appendix: Applications
A.1 Heat Conduction
A.2 Flow in Porous Media
A.3 Continuum Mechanics
Bibliography
Index
