论文标题
具有声音边界的半导体的内部亚音速稳态对流体动力模型的结构稳定性
Structural stability of interior subsonic steady-states to hydrodynamic model for semiconductors with sonic boundary
论文作者
论文摘要
对于以Euler-Poisson方程为代表的具有声音边界的半导体的固定流体动力模型，它具有各种物理溶液，包括内部亚音线解决方案/内部超音速解决方案/冲击透射溶液/$ C^1 $ -Smoth-smooth Transonic Solutions。但是，这些物理解决方案的结构稳定性是具有挑战性的，众所周知，它仍然是开放的。在本文中，我们研究了掺杂谱在亚音速区域受到限制时内部亚音速溶液的结构稳定性。主要结果是通过使用局部（加权）奇异性分析和单调性论点来证明的。结果本身和这里开发的技术都将使我们对我们对其余解决方案类型的结构稳定性的后续研究进行一些真正的启发性见解。
For the stationary hydrodynamic model for semiconductors with sonic boundary, represented by Euler-Poisson equations, it possesses the various physical solutions including interior subsonic solutions/interior supersonic solutions/shock transonic solutions/$C^1$-smooth transonic solutions. However, the structural stability for these physical solutions is challenging and has remained open as we know. In this paper, we investigate the structural stability of interior subsonic solutions when the doping profiles are restricted in the subsonic region. The main result is proved by using the local (weighted) singularity analysis and the monotonicity argument. Both the result itself and techniques developed here will give us some truly enlightening insights into our follow-up study on the structural stability of the remaining types of solutions.
