Hyperbolic Systems of Conservation Laws The One-Dimensional Cuachy Problem [Hardcover]

This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This volume is the first to present a comprehensive account of these new, fundamental advances. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. A set of problems, with varying difficulty is given at the end of each chapter to verify and expand understanding of the concepts and techniques previously discussed. For researchers, this book will provide an indispensable reference to the state of the art in the field of hyperbolic systems of conservation laws.

1. Introduction
2. Mathematical preliminaries
3. Semilinear and quasilinear systems
4. Discontinuous solutions
5. The Riemann problem
6. The single conservation law
7. The Cauchy problem for systems
8. Stability
9. Uniqueness
10. Qualitative properties
11. Bibliographical notes
Index

Hyperbolic systems of conservation laws has become such a mature topic in the past decade that several researchers decided to write a book on the subject recently. . This book is entirely devoted to the achievements of the author's long-standing program. The author's results have been the most impressive obtained about conservation laws in the past decade. . .Bressan's style is fluid, and several exercises help doctoral students to digest each chapter. . .Presumably, this book will be often cited in research papers on hyperbolic conservation laws. It is recommended to researchers and graduate l³(