Asymptotic Behavior of Solutions for p-System with Relaxation
Author: Zhu, C.
Source: Journal of Differential Equations, Volume 180, Number 2, April 2002 , pp. 273-306(34)
Publisher: Academic Press
Abstract:In this paper, we consider the asymptotic behavior of solutions for the Cauchy problem for p-system with relaxationvt-ux=0,Eut+p(v)x=1 (f(v)-u),with initial dataI(v, u)(x, 0)=(v 0(x), u 0(x))→(v±, u±), v±>0, as x→± ∞.We are interested to show the solutions of (E), (I) tend also to the equilibrium rarefaction waves and the traveling waves even if the limits (v±, u±) of the initial data at x=±∞ do not satisfy the equilibrium equation; i.e., u±≠f(v±). When the limits of the initial data at infinity satisfy equilibrium states, Liu  studied the stability of rarefaction waves and traveling waves for the general 2×2 hyperbolic conservation laws with relaxation. © 2002 Elsevier Science (USA).
Document Type: Research Article
Affiliations: Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan, 430079, People's Republic of China
Publication date: 2002-04-01