Convergence to nonlinear diffusion waves for solutions of p-system with time-dependent damping
Convergence to nonlinear diffusion waves for solutions of p-system with time-dependent damping
复制标题
具有瞬态阻尼的 p 系统解的非线性扩散波收敛
DOI：
10.1016/j.jmaa.2017.07.025
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发表时间：
2017
影响因子：
1.3
通讯作者：
Zhang Kaijun
中科院分区：
文献类型：
--
作者：
Li Haitong;Li Jingyu;Mei Ming;Zhang Kaijun
本文研究了具有时间渐退化阻尼项−1 (1+ t) λ u为0≤λ< 1的双曲型p-系统的Cauchy问题，证明了该阻尼p-系统有一对唯一的全局解，且这些解随时间渐近地趋向于位移的非线性扩散波，即对应的受达西定律支配的非线性抛物方程的解。我们进一步推导了初始扰动在l2时的收敛速率。所采用的方法是技术性时间加权能量法。
In this paper, we study the Cauchy problem for the hyperbolic p-system with time-gradually-degenerate damping term− 1 (1+ t) λ u for 0⩽ λ< 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.