| My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose, then the book should be found usable both as a text for students and as a source of reference for the more advanced mathematician. I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few places where my nomenclature differs from that in the existing literature of measure theory, I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are, for instance, sound algebraic reasons for using the terms "lattice" and "ring" for certain classes of sets--reasons which are more cogent than the similarities that caused Hausdorff to use "ring" and "field." 本书为英文版。 |
| 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 |
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