Abstract :
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.
Keywords :
convergence rate , Asymptotic profile , relaxation , asymptotic behavior
