Hyperbolic Systems of Conservation Laws: The One-Dimensional Cuachy Problem

by Alberto Bressan

Overview

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.

Product Details

ISBN-13:	9780198507000
Publisher:	Oxford University Press
Publication date:	12/21/2000
Series:	Oxford Lecture Series in Mathematics and Its Applications , #20
Edition description:	New Edition
Pages:	262
Product dimensions:	9.21(w) x 6.14(h) x 0.63(d)

About the Author

International School for Advanced Studies

Table of Contents

1. Introduction2. Mathematical preliminaries3. Semilinear and quasilinear systems4. Discontinuous solutions5. The Riemann problem6. The single conservation law7. The Cauchy problem for systems8. Stability9. Uniqueness10. Qualitative properties11. Bibliographical notesIndex

Editorial Reviews

"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 students who specialize in this field."—Mathematical Review

From the Publisher