Large time behavior and quasineutral limit of solutions to a bipolar hydrodynamic modelwith large data and vacuum
Large time behavior and quasineutral limit of solutions to a bipolar hydrodynamic modelwith large data and vacuum
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DOI：
10.3934/dcds.2009.24.455
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发表时间：
2009-03
影响因子：
1.1
通讯作者：
F. Huang;Yeping Li
中科院分区：
文献类型：
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作者：
F. Huang;Yeping Li
本文考虑一维双极流体动力学模型。该系统采用欧拉-泊松形式，在动量方程中加入电场和摩擦阻尼。首次研究了双极流体动力学模型的L ∞熵解的大时间行为。以往的工作主要是研究光滑解，其中没有真空发生，初始数据是小的。本文证明了任何有界熵解都强收敛于L2（R）中多孔介质方程或热方程的相似解，并随时间衰减。初始数据可以包含真空，并且可以是任意大的。该方法也被应用于改善[F.Huang，R.Pan，Arch. Rational Mech. Anal.，166（2003），359 -376]中给出的解。作为副产品，证明了双极流体动力学模型的有界L ∞熵解收敛于阻尼为$t\rightarrow\infty$的欧拉方程的熵解。
In this paper, a one-dimensional bipolar hydrodynamic model is considered. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. The large time behavior of L ∞ entropy solutions of the bipolar hydrodynamic model is firstly studied. Previous works on this topic are mainly concerned with the smooth solution in which no vacuum occurs and the initial data is small. It is proved in this paper that any bounded entropy solution strongly converges to the similarity solution of the porous media equation or the heat equation in L 2(R) with time decay rate. The initial data can contain vacuum and can be arbitrarily large. The method is also applied to improve the convergence rate of [F.Huang, R.Pan, Arch. Rational Mech. Anal.,166(2003),359-376] for compressible Euler equations with damping. As a by product, it is shown that the bounded L ∞ entropy solution of the bipolar hydrodynamic model converges to the entropy solution of Euler equations with damping as $t\rightarrow\infty$.