Well-posedness for hyperbolic systems of conservation laws with large BV data
type: Item
instance of: scholarly article
title: Well-posedness for hyperbolic systems of conservation laws with large BV data
zbMATH Open document ID: 1065.35189
author: Marta Lewicka
published in: Archive for Rational Mechanics and Analysis
publication date: 2005-03-02T00:00:00Z
review text: The author studies the Cauchy problem for a strictly hyperbolic \(n\times n\) system of conservation laws \(u_t+f(u)_x=0\). It is required that each characteristic field of this system is either genuinely nonlinear or linearly degenerate. The initial data \(u(0,x)=\bar u(x)\) is assumed to have bounded but possibly large total variation. Under some linearized stability condition the author utilizes the wave-front-tracking algorithm and proves existence and uniqueness of a (local in time) BV-solution. Moreover, the Lyapunov functional is constructed, which yields existence of a Lipschitz continuous flow of solutions. The last section contains some applications to the system of gas dynamics.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 2140277
zbMATH Keywords: BV-solutions
zbMATH Keywords: Riemann solutions
zbMATH Keywords: stability conditions
zbMATH Keywords: Lyapunov functional
reviewed by: Evgeniy Panov
MaRDI profile type: Publication
full work available at URL: s00205-004-0325-6
OpenAlex ID: W2017803119
cites work: On the front-tracking algorithm
cites work: Vanishing viscosity solutions of nonlinear hyperbolic systems
cites work: Q4490854
cites work: Unique solutions of 2 X 2 conservation laws with large data
cites work: Well-posedness of the Cauchy problem for 𝑛×𝑛 systems of conservation laws
cites work: \(L^1\) stability estimates for \(n\times n\) conservation laws
cites work: A variational calculus for discontinuous solutions of systems of conservation laws
cites work: Q5313837
cites work: Front tracking for hyperbolic conservation laws
cites work: Hyperbolic systems of conservation laws II
cites work: \(L^1\) stability of patterns of non-interacting large shock waves
cites work: Stability conditions for patterns of noninteracting large shock waves
cites work: Lyapunov Functional for Solutions of Systems of Conservation Laws Containing a Strong Rarefaction
cites work: Stability Conditions for Strong Rarefaction Waves
cites work: The stability of multidimensional shock fronts
cites work: Q4222728
cites work: Sufficient conditions for local existence via Glimm's scheme for large BV data
cites work: Q4314474
DOI: 10.1007/S00205-004-0325-6
Recommended article: Q2751137
Recommended article: Well-Posedness for a Class of Hyperbolic Systems of Conservation Laws in Several Space Dimensions
Recommended article: Q4247613
Recommended article: Q4736221
Recommended article: Large-time behavior of solutions for hyperbolic-parabolic systems of conservation laws
Recommended article: Large-time behaviour of solutions to hyperbolic–parabolic systems of conservation laws and applications
Recommended article: Q4693925
Recommended article: BV Solutions to Hyperbolic Conservation Laws
Recommended article: Q4204548
Recommended article: Q4462297
description: scientific article; zbMATH DE number 2140277