The Cauchy problem for hyperbolic conservation laws with three equations
type: Item
instance of: scholarly article
title: The Cauchy problem for hyperbolic conservation laws with three equations
zbMATH Open document ID: 0862.35069
author: C. Klingenberg
author: Yun-Guang Lu
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-11-13T00:00:00Z
review text: The authors consider the Cauchy problem for the nonlinear system \[ v_t-u_x=0,\quad u_t-\sigma(v,s)_x+\alpha u=0,\quad s_\sigma+ {\beta\cdot\{s-f(v)\}\over\tau}=0 \] with bounded \(L^2\) measurable initial data \((v,u,s)|_{t=0}= (v_0(x),u_0(x),s_0(x))\). They prove existence of the global generalized solution for the case \(\beta=0\). Moreover, they show that the solution of the equilibrium system \[ v_t-u_x=\sigma,\quad u_t-\sigma(v,f(v))_x+\alpha u=0 \] is given by the limit of the solutions of viscous approximations as the dissipation and the reaction time \(\tau\) go to zero in the case \(\beta>0\).
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 930250
zbMATH Keywords: zero relaxation limit
zbMATH Keywords: global generalized solution
reviewed by: Jinghua Wang
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0313
OpenAlex ID: W2001691765
DOI: 10.1006/JMAA.1996.0313
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description: scientific article; zbMATH DE number 930250