Transonic shock solutions for a system of Euler-Poisson equations
Transonic shock solutions for a system of Euler-Poisson equations
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DOI：
10.4310/cms.2012.v10.n2.a1
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发表时间：
2012-06
影响因子：
1
通讯作者：
T. Luo;Z. Xin
中科院分区：
文献类型：
--
作者：
T. Luo;Z. Xin
考虑了模拟半导体器件或等离子体的Euler-Poisson方程组的边值问题。边界条件为超音速进流和亚音速出流。本文的目的是阐明电场在具有跨音速激波的溶液结构中所起的作用。根据边界数据和物理间隔长度的不同情况，得到了跨音速激波解的存在性、不存在性、唯一性和非唯一性。给出了求解的详细结构。激波位置由边界数据确定。固定正电背景离子密度处于超音速和亚音速时，在不同的情况下表现出不同的现象。
A boundary value problem for a system of Euler-Poisson equations modeling semiconductor devices or plasma is considered. The boundary conditions are supersonic inflow and subsonic outflow. The purpose of this paper is to elucidate the role played by the electric field in the structure of solutions with transonic shocks. The existence, non-existence, uniqueness, and non-uniqueness of solutions with transonic shocks are obtained according to the different cases of boundary data and physical interval length. Detailed structures of solutions are given. Shock locations are determined by the boundary data. Different phenomena are shown for the different situations when the density of fixed, positively charged background ions is in supersonic and subsonic regimes.