Structural Stability of Supersonic Solutions to the Euler-Poisson System
Structural Stability of Supersonic Solutions to the Euler-Poisson System
复制标题
欧拉-泊松系统超声速解的结构稳定性
DOI：
10.1007/s00205-020-01583-7
复制
发表时间：
2021
影响因子：
2.5
通讯作者：
Xie Chunjing
中科院分区：
文献类型：
--
作者：
Bae Myoungjean;Duan Ben;Xiao Jingjing;Xie Chunjing
本文建立了二维半导体器件和等离子体流体动力学模型的Euler-Poisson方程组在通道入口处水平方向的流速和电场扰动下超声速解的结构稳定性。首先，将超声速区的Euler-Poisson方程组转化为二阶双曲-椭圆耦合方程组，并与几个输运方程一起求解。分析的关键成分之一是获得相关的线性化双曲椭圆耦合系统的边值问题的适定性，这是通过一个微妙的选择乘子获得能量估计。将双曲-椭圆方程组的估计与迭代法相结合，建立了一般情况下超音速解的非线性结构稳定性。
The structural stability for supersonic solutions of the Euler–Poisson system for hydrodynamical model in semiconductor devices and plasmas in two dimensional domain is established, under the perturbation of the flow velocity and the strength of electric field in the horizontal direction at the entrance of a channel. First, the Euler–Poisson system in the supersonic region is reformulated into a second order hyperbolic–elliptic coupled system together with several transport equations. One of the key ingredients of the analysis is to obtain the well-posedness of the boundary value problem for the associated linearized hyperbolic–elliptic coupled system, which is achieved via a delicate choice of multiplier to gain energy estimate. The nonlinear structural stability of supersonic solution in the general situation is established by combining the iteration method with the estimate for hyperbolic–elliptic system and the transport equations together.