The well-posedness for the supersonic solutions of the Euler-Poisson system for hydrodynamical model in semiconductor devices and plasmas is studied in this paper. We first reformulate the Euler-Poisson system in the supersonic region 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.

中文翻译：

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欧拉-泊松系统超音速解的结构稳定性

本文研究了半导体器件和等离子体中流体动力学模型的欧拉-泊松系统超声速解的适定性。我们首先将超音速区域中的 Euler-Poisson 系统重新表述为一个二阶双曲-椭圆耦合系统以及几个传输方程。分析的关键要素之一是获得相关线性化双曲-椭圆耦合系统的边界值问题的适定性，这是通过精心选择乘法器来获得能量估计来实现的。将迭代法与双曲-椭圆系统估计和输运方程相结合，建立了一般情况下超声速解的非线性结构稳定性。