激波和反应扩散方程（第2版）（英文版）

For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in constructing travelling waves for systems of nonlinear equations. The final section, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applicable to many interesting reaction-diffusion systems.

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