Nonlinear diffusion waves for hyperbolic p-system with nonlinear damping
Nonlinear diffusion waves for hyperbolic p-system with nonlinear damping
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DOI：
10.1016/j.jde.2009.04.004
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发表时间：
2009-08
影响因子：
2.4
通讯作者：
Ming Mei
中科院分区：
文献类型：
--
作者：
Ming Mei
本文研究具有非线性阻尼的p-双曲型守恒律方程组。当常数状态较小时，阻尼p-系统的Cauchy问题的解整体存在并收敛于其相应的非线性扩散波，即由Darcy定律给出的相应非线性抛物方程的解.最优收敛速度也得到了。为了克服非线性阻尼带来的困难，技术上构造了一对修正函数。所采用的方法是基本能量法和绿色函数逼近技术。另一方面，当常数态很大时，p-系统的柯西问题的解将在有限时刻爆破。
This paper is concerned with the p-system of hyperbolic conservation laws with nonlinear damping. When the constant states are small, the solutions of the Cauchy problem for the damped p-system globally exist and converge to their corresponding nonlinear diffusion waves, which are the solutions of the corresponding nonlinear parabolic equation given by the Darcy's law. The optimal convergence rates are also obtained. In order to overcome the difficulty caused by the nonlinear damping, a couple of correction functions have been technically constructed. The approach adopted is the elementary energy method together with the technique of approximating Green function. On the other hand, when the constant states are large, the solutions of the Cauchy problem for the p-system will blow up at a finite time.