Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping

In this paper, we study the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v(x,t),u(x,t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave (-v(x, t), -u(x, t)) governed by the classical Darcy's law provided that the corresponding prescribed initial error function (w0(x), z0(x))lies in (H3 × H2) (R) and |v+ - v-| + ‖w0‖3 + ‖z0‖2 is sufficiently small.Furthermore, the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions are also obtained.

作 者： ZHU Changjiang JIANG Mina   作者單位： Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, China  刊 名： 中國科學A輯（英文版）  SCI 英文刊名： SCIENCE IN CHINA (SERIES A)  年，卷(期)： 2006 49(6)  分類號： O1  關鍵詞： nonlinear damping   nonlinear diffusion waves   convergence rates   energy estimates  

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