Asymptotic Behavior of Solutions for p-System with Relaxation
Asymptotic Behavior of Solutions for p-System with Relaxation
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DOI：
10.1006/jdeq.2001.4063
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发表时间：
2002-04
影响因子：
2.4
通讯作者：
Changjiang Zhu
中科院分区：
文献类型：
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作者：
Changjiang Zhu
本文考虑具松弛项的p-系统柯西问题解的渐近性态，其中vt−ux=0，ut+p(V)x=1e(f(V)−u)，(E)，初值为(v，u)(x，0)=(v0(X)，u0(X))→(v±，u±)，v±>；0，asx→±∞.(I)即使在x=±∞的初值极限(v±，u±)不满足平衡方程，即u±≠f(v±)时，(E)，(I)的解也趋向于平衡稀疏波和行波。当初值在无穷远处的极限满足平衡态时，刘[9]研究了一般的2×2松弛双曲型守恒律的稀疏波和行波的稳定性。
In this paper, we consider the asymptotic behavior of solutions for the Cauchy problem for p-system with relaxationvt−ux=0,ut+p(v)x=1e(f(v)−u), (E) with initial data(v, u)(x, 0)=(v 0(x), u 0(x))→(v±, u±), v±>0,asx→± ∞. (I) 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 [9] studied the stability of rarefaction waves and traveling waves for the general 2×2 hyperbolic conservation laws with relaxation.