Asymptotic behavior of solutions for p-system with relaxation

In this paper, we consider the asymptotic behavior of solutions for the Cauchy problem for p-system with relaxation v(t) - u(x) = 0, u(l) + p(v)(x) = 1/3(f(v) - u), with initial data (v, u)(x, 0) = (v(0)(x), u(0)(x)) --> (v(+/-), u(+/-)), v(+/-) > 0, as x --> infinity. 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 = +/-infinity not satisfy the equilibrium equation; i.e., u(+/-) not equal 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 x 2 hyperbolic conservation laws with relaxation. (C) 2002 Elsevier Science (USA).