Convergence to nonlinear diffusion waves for solutions of p-system with time-dependent damping

[摘要] In this paper, we study the Cauchy problem for the hyperbolic p-system with time gradually-degenerate damping term -1/(1+t)(lambda)u for 0 <= lambda < 1, and show that the damped p-system has a couple of global solutions uniquely, and such solutions tend time-asymptotically to the shifted nonlinear diffusion waves, which are the solutions of the corresponding nonlinear parabolic equation governed by the Darcy's law. We further derive the convergence rates when the initial perturbations are in L-2. The approach adopted is the technical time-weighted energy method. (C) 2017 Elsevier Inc. All rights reserved.

[发布日期] 2017-12-15

[关键词] Time-dependent damping;Nonlinear diffusion waves;Convergence rates;Time-weighted energy estimates