Radial solutions of hydrodynamic model of semiconductors with sonic boundary
Radial solutions of hydrodynamic model of semiconductors with sonic boundary
复制标题
声波边界半导体流体动力学模型的径向解
DOI：
10.1016/j.jmaa.2021.125187
复制
发表时间：
2021
影响因子：
1.3
通讯作者：
Kaijun Zhang
中科院分区：
文献类型：
--
作者：
Liang Chen;Ming Mei;Guojing Zhang;Kaijun Zhang
本文研究了以欧拉-泊松方程为代表的具有声波边界的半导体多维定常流体力学模型。证明了具有音速边界的定常Euler-Poisson方程具有唯一的亚音速解和至少一个径向形式的超音速解。采用的证明方法是能量法结合紧性分析。对于一维径向超声速解，由于受到多个维度的影响和声波边界的限制，获得关键的能量估计更具挑战性，我们提出了一种全新的两步迭代方案来建立关键的能量估计。这是首次尝试研究具有声波边界的一维定常流，所得结果在本质上改进和发展了以往一维定常流的研究。
The purpose of this paper is to study the multi-dimensional steady hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary. We prove that, the steady Euler-Poisson equations with sonic boundary possess a unique subsonic solution and at least one supersonic solution in the radial form. The adopted approach for proof is the energy method combining the compactness analysis. For then-D radial supersonic solutions, since it is more challenging to get the crucial energy estimates due to the effect by the multiple dimensions and the restriction by the sonic boundary, we propose a brand new two-steps iteration scheme to build up the key energy estimates. This is the first attempt to study then-D steady-states with the sonic boundary, and the results obtained essentially improve and develop the previous studies in the one-dimensional case.