Stability of periodic steady-state solutions to a non-isentropic Euler Poisson system
Stability of periodic steady-state solutions to a non-isentropic Euler Poisson system
复制标题
非等熵欧拉泊松系统周期性稳态解的稳定性
DOI：
10.1016/j.jde.2017.02.002
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发表时间：
2017
影响因子：
2.4
通讯作者：
Peng Yue-Jun
中科院分区：
文献类型：
--
作者：
Liu Cunming;Peng Yue-Jun
研究了一类不含温度阻尼项的非等熵Euler-Poisson系统在非常数稳态附近的周期光滑解的稳定性。该系统产生于半导体理论中，对于该理论，掺杂分布是给定的光滑函数。在这个稳定性问题中，对掺杂分布的大小没有特殊的限制，而只对微扰的大小有限制。证明了周期定态的小扰动在大时间内是指数稳定的。为此，我们引入了新的变量，并选择了完整欧拉方程的非对角对称化来恢复耗散估计。这也使得稳定性结果的证明变得非常简单和简洁。
We study the stability of periodic smooth solutions near non-constant steady-states for a non-isentropic Euler–Poisson system without temperature damping term. The system arises in the theory of semiconductors for which the doping profile is a given smooth function. In this stability problem, there are no special restrictions on the size of the doping profile, but only on the size of the perturbation. We prove that small perturbations of periodic steady-states are exponentially stable for large time. For this purpose, we introduce new variables and choose a non-diagonal symmetrizer of the full Euler equations to recover dissipation estimates. This also allows to make the proof of the stability result very simple and concise.