Analysis of Systems of Conservation Laws: 1st Edition (Hardback) book cover

Analysis of Systems of Conservation Laws

1st Edition

Edited by Heinrich Freistuhler

Chapman and Hall/CRC

272 pages

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Hardback: 9780849306440
pub: 1998-12-30
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Description

Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in successful research activity.

The EU-TMR network "Hyperbolic Systems of Conservation Laws held a summer program offering short courses on the Analysis of Systems of Conservation Laws. This book contains five of the self-contained short courses presented during this program by experts of international reputation. These courses, which address solutions to hyperbolic systems by the front tracking method, non-strictly hyperbolic conservation laws, hyperbolic-elliptic coupled systems, hyperbolic relaxation problems, the stability of nonlinear waves in viscous media and numerics, and more, represent the state of the art of most central aspects of the field.

Table of Contents

Preface

Analysis of Solutions to Hyperbolic Systems by the Front Tracking Method, A. Bressan, Scuola Internazionale Superiore di Studi Avanzati, Trieste

A Wave-Front Tracking Algorithm

Continuous Dependence on Initial Data

A Front Tracking Algorithm for 2 x 2 Systems

Uniqueness of the Standard Riemann Semigroup

Characterization of Semigroup Trajectories

Unique Solutions to the Cauchy Problem

References

Hyperbolic Conservation Laws, P.T. Kan, Purdue University, Indianapolis, Indiana

Global Solutions to Systems with Umbilic Degeneracy

Introduction

General Classes and a Canonical Family of Degenerate Systems

Parabolic Approximation and Young Measures

Entropy Functions and Entropy Dissipation Measures

Cm Goursat Entropies

Convergence of Approximate Solutions

Initial Boundary Value Problems in L8

Introduction

Boundary Sets

Godunov Schemes for IBVP

Traces of Entropy Fluxes

Godunov Schemes for Scalar Equations: Interior and Boundary Regularity

The Study of Boundary Layers

A Class of Quadratic Systems and a Class of Well-Posed IBVP

References

The Initial Value Problem for Hyperbolic-Elliptic Coupled Systems and Applications to Radiation Hydrodynamics, S. Kawashima, Y. Nikkuni, S. Nishibata, Kyushu University, Fukuoka

Introduction

Entropy Function and Symmetrization

Local Existence

Stability Condition

Global Existence

Proof of a Priori Estimate

Decay Properties for the Linearized System

Decay Estimate

Large-Time Approximation

Applications

References

Recent Results on Hyperbolic Relaxation Problems, R. Natalini, Istituto per le Applicazioni del Calcolo, Rome, Italy

Introduction

Motivations

The Smooth Case

Discontinuous Equilibrium Solutions and Weak Convergence Methods

The BV Framework

References

Lectures on Stability of Nonlinear Waves in Viscous Media and Numerics, A. Szepessy, Kungl. Tekniska Högskolan, Stockholm

Introduction

Perturbations of Constant States

Shock Waves

Rarefaction Waves

Multigrid Methods for Flow Problems

References

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics