Cauchy problem for quasilinear hyperbolic systems
type: Item
instance of: scholarly article
title: Cauchy problem for quasilinear hyperbolic systems
zbMATH Open document ID: 0959.35003
published in: MSJ Memoirs
publication date: 2000-12-14T00:00:00Z
full work available at URL: http://projecteuclid.org/euclid.msjm/1389985988
review text: This Memoir provides a careful and comprehensive account of the Cauchy problem for quasilinear hyperbolic systems. Included among the many applications of such systems are gas dynamics, shallow water theory, nonlinear elasticity and acoustics. The questions addressed in this Memoir, that contains four major chapters, are: 1. Under what conditions does the Cauchy problem for such systems admit a unique global classical solution 2. Under what conditions does the Cauchy problem for such systems blow up, and when and where does this occur 3. How do singularities develop from smooth initial data, and what can be said about the stability of such singularities, included amongst which are shocks. The account that is clearly written, and contains a comprehensive bibliography, provides an excellent introduction to the subject.
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35L60
zbMATH DE Number: 1544071
zbMATH Keywords: gas dynamics
zbMATH Keywords: shallow water theory
zbMATH Keywords: nonlinear elasticity
zbMATH Keywords: acoustics
zbMATH Keywords: unique global classical solution
zbMATH Keywords: blow up
author: De-Xing Kong
reviewed by: Alan Jeffrey
MaRDI profile type: Publication
OpenAlex ID: W632918734
DOI: 10.2969/MSJMEMOIRS/006010000
description: scientific article; zbMATH DE number 1544071