Lp-convergence rate to diffusion waves for p-system with relaxation

In this paper, we consider the asymptotic behavior of solution for the Cauchy problem for p-system with relaxation vt − ux = 0, ut + p(v)x = 1 ε (f (v)− u), (E) with initial data (v,u)(x, 0) = v0(x),u0(x) →(v0,u±), as x→±∞. (I) By applying the elementary energy method and the Green function method for the parabolic equation, we obtain the Lp-convergence rate to the diffusion waves for the Cauchy problem (E), (I).  2002 Elsevier Science (USA). All rights reserved.