Global \textbf{BV} entropy solutions and uniqueness for hyperbolic systems of balance laws
type: Item
instance of: scholarly article
title: Global \textbf{BV} entropy solutions and uniqueness for hyperbolic systems of balance laws
zbMATH Open document ID: 1024.35066
author: Debora Amadori
author: Laurent Gosse
author: Graziano Guerra
published in: Archive for Rational Mechanics and Analysis
publication date: 2002-07-29T00:00:00Z
review text: The authors consider the Cauchy problem for \(n \times n\) strictly hyperbolic systems of nonresonant balance laws \[ \begin{aligned} u_t+f(u)_x &= g(x,u), \qquad x \in \mathbb R, t>0, \\ u(0,.) &= u_o \in L^1 \cap \text{BV} (\mathbb Ri; {\mathbb R}^n), \\ |\lambda_i(u)|&\geq c > 0 \text{ for all } i\in \{1,\ldots,n\}, \\ |g(.,u)|+ \|\nabla_u g(.,u) \|&\leq \omega \in L^1 \cap L^\infty (\mathbb Ri), \end{aligned} \] each characteristic field being genuinely nonlinear or linearly degenerate. Assuming that \(\|\omega \|_{L^1(\mathbb R)}\) and \(\|u_0 \|_{\text{BV}(\mathbb R)}\) are small enough, the authors prove the existence and uniqueness of global entropy solutions of bounded total variation as limits of special wave-front tracking approximations for which the source term is localized by means of Dirac masses. Moreover, they give a characterization of the resulting semigroup trajectories in terms of integral estimates.
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 1773416
zbMATH Keywords: non-resonance condition
zbMATH Keywords: Riemann solvers
zbMATH Keywords: wave-front tracking algorithm
reviewed by: Evgeniy Panov
MaRDI profile type: Publication
full work available at URL: s002050200198
OpenAlex ID: W2044381590
DOI: 10.1007/S002050200198
description: scientific article; zbMATH DE number 1773416