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

AbstractIn this paper, we consider the asymptotic behavior of solution for the Cauchy problem for p-system with relaxation (E)vt−ux=0,ut+p(v)x=1ε(f(v)−u), with initial data (I)(v,u)(x,0)=v0(x),u0(x)→(v0,u±),asx→±∞. 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)