《激波和反應擴散方程》是1999年世界圖書出版公司出版的圖書，作者是J.Smoller。
基本介紹
- 書名：激波和反應擴散方程
- 作者：J.Smoller
- ISBN：9787506241007
- 頁數：632
- 定價：79.00元
- 出版社：世界圖書出版公司
- 出版時間：1999-3
內容簡介,目錄,
內容簡介
我在這本書的主要目的是提出一個統一的治療方法，這一部分的測量理論，近年來已顯示出自己是最有用的，它在現代分析中的套用。如果我達到了我的目的，那么這本書應該被發現可以作為一個學生的文本和作為一個更高級的數學家的參考來源。
我試圖保持一個最小的新的和不尋常的術語和符號的數量。在我的命名不同的幾個地方，在現有的文獻中的測量理論，我的動機是試圖協調與其他部分的數學的使用。有，例如，聲音代數原因使用術語“格”和“環”為某些類別的集合--原因是更切實比相似之處導致Hausdorff使用“環”和“場”。
目錄
Acknowledgment
Preface to the Second Edition
Preface to the First Edition
List of Frequently Used Symbols
PART Ⅰ Basic Linear Theory
CHAPTER 1 lll-Posed Problems
CHAPTER 2 Characteristics and Initial-Value Problems
CHAPTER 3 The One-Dimensional Wave Equation
CHAPTER 4 Uniqueness and Energy Integrals
CHAPTER 5 Holmgren's Uniqueness Theorem
CHAPTER 6 An Initial-Value Problem for a Hyperbolic Equation
CHAPTER 7 Distribution Theory
CHAPTER 8 Second-Order Linear Elliptic Equations
CHAPTER 9 Second-Order Linear Parabolic Equations
PART ⅡReaction-Diffusion Equations
CHAPTER 10 Comparison Theorems and Monotonicity Methods
CHAPTER 11 Linearization
CHAPTER 12 Topological Methods
CHAPTER 13 Bifurcation Theory
CHAPTER 14 Systems of Reaction-Diffusion Equations
PART Ⅲ The Theory of Shock Waves
CHAPTER 15 Discontinuous Solutions of Conservation Laws
CHAPTER 16 The Single Conservation Law
CHAPTER 17 The Riemann Problem for Systems ofConservation Laws
CHAPTER 18 Applications to Gas Dynamics
CHAPTER 19 The Glimm Difference Scheme
CHAPTER 20 Riemann Invariants. Entropy. and Uniqueness
CHAPTER 21 Quasi-Linear Parabolic Systems
PART Ⅳ The Conley Index
CHAPTER 22 The Conley Index
CHAPTER 23 Index Pairs and the Continuation Theorem
CHAPTER 24 Travelling Waves
CHAPTER 25 Recent Results
Bibliography
Author Index
Subject Index
Preface to the Second Edition
Preface to the First Edition
List of Frequently Used Symbols
PART Ⅰ Basic Linear Theory
CHAPTER 1 lll-Posed Problems
CHAPTER 2 Characteristics and Initial-Value Problems
CHAPTER 3 The One-Dimensional Wave Equation
CHAPTER 4 Uniqueness and Energy Integrals
CHAPTER 5 Holmgren's Uniqueness Theorem
CHAPTER 6 An Initial-Value Problem for a Hyperbolic Equation
CHAPTER 7 Distribution Theory
CHAPTER 8 Second-Order Linear Elliptic Equations
CHAPTER 9 Second-Order Linear Parabolic Equations
PART ⅡReaction-Diffusion Equations
CHAPTER 10 Comparison Theorems and Monotonicity Methods
CHAPTER 11 Linearization
CHAPTER 12 Topological Methods
CHAPTER 13 Bifurcation Theory
CHAPTER 14 Systems of Reaction-Diffusion Equations
PART Ⅲ The Theory of Shock Waves
CHAPTER 15 Discontinuous Solutions of Conservation Laws
CHAPTER 16 The Single Conservation Law
CHAPTER 17 The Riemann Problem for Systems ofConservation Laws
CHAPTER 18 Applications to Gas Dynamics
CHAPTER 19 The Glimm Difference Scheme
CHAPTER 20 Riemann Invariants. Entropy. and Uniqueness
CHAPTER 21 Quasi-Linear Parabolic Systems
PART Ⅳ The Conley Index
CHAPTER 22 The Conley Index
CHAPTER 23 Index Pairs and the Continuation Theorem
CHAPTER 24 Travelling Waves
CHAPTER 25 Recent Results
Bibliography
Author Index
Subject Index
