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

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

by Alberto Bressan
     
 

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

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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.

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Product Details

ISBN-13:
9780198507000
Publisher:
Oxford University Press, USA
Publication date:
12/28/2000
Series:
Oxford Lecture Series in Mathematics and Its Applications Series, #20
Edition description:
New Edition
Pages:
264
Sales rank:
1,268,785
Product dimensions:
6.00(w) x 9.20(h) x 0.80(d)

Table of Contents

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

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