Convergence Rates to Nonlinear Diffusion Waves for Solutions to the System of Compressible Adiabatic Flow through Porous Media
Shifeng Geng, Zhen Wang · Communications in Partial Differential Equations · 2010
We realize the best asymptotic profile for the solutions to the Cauchy problem of the nonisentropic p-system with damping is a particular solution to the corresponding nonlinear parabolic equation with special initial data, and we further show the convergence rates to this particular asymptotic profile. This new rates are much better than that obtained by Nishihara and Nishikawa [15 Nishihara , K. , Nishikawa , M. ( 2001 ). Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media . SIAM J. Math. Anal. 33 : 216 – 239 . [Google Scholar]].