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作者:

Feng, Yue-Hong (Feng, Yue-Hong.) | Mei, Ming (Mei, Ming.) | Zhang, Guojing (Zhang, Guojing.)

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摘要:

For unipolar hydrodynamic model of semiconductor device represented by Euler-Poisson equations, when the doping profile is supersonic, and the boundary data are in subsonic region and supersonic region separately, the system possesses the shock transonic steady-states and the smooth transonic steady-states. In this paper we study the nonlinear structural stability and the linear dynamic instability of these steady transonic solutions. For any relaxation time: 0 < t <= +infinity , by means of elaborate singularity analysis, we first investigate the structural stability of the C-1-smooth transonic steady-states, once the perturbations of the initial data and the doping profiles are small enough. We note that, when the C-1-smooth transonic steady-states pass through the sonic line, they produce singularities for the system, and cause some essential difficulty in the proof of structural stability. Moreover, when the relaxation time is large enough t >> 1, under the condition that the electric field is positive at the shock location, we prove that the transonic shock steady-states are structurally stable with respect to small perturbations of the supersonic doping profile. Furthermore, we show the linearly dynamic instability for these transonic shock steady-states provided that the electric field is suitable negative. The proofs for the structural stability results are based on singularity analysis, a monotonicity argument on the shock position and the downstream density, and the stability analysis of supersonic and subsonic solutions. The linear dynamic instability of the steady transonic shock for Euler- Poisson equations can be transformed to the ill-posedness of a free boundary problem for the Klein-Gordon equation. By using a nontrivial transformation and the shooting method, we prove that the linearized problem has a transonic shock solution with exponential growths. These results enrich and develop the existing studies. (c) 2022 Elsevier Inc. All rights reserved.

关键词:

C-1- smooth transonic solutions Linear dynamic instability Euler-Poisson equations Structural stability Transonic shock solutions Hydrodynamic model of semiconductors

作者机构:

  • [ 1 ] [Feng, Yue-Hong]Beijing Univ Technol, Fac Sci, Coll Math, Beijing 100022, Peoples R China
  • [ 2 ] [Mei, Ming]Champlain Coll St Lambert, Dept Math, Quebec City, PQ J4P 3P2, Canada
  • [ 3 ] [Feng, Yue-Hong]McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada
  • [ 4 ] [Mei, Ming]McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada
  • [ 5 ] [Zhang, Guojing]Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

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来源 :

JOURNAL OF DIFFERENTIAL EQUATIONS

ISSN: 0022-0396

年份: 2023

卷: 344

页码: 131-171

2 . 4 0 0

JCR@2022

ESI学科: MATHEMATICS;

ESI高被引阀值:9

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WoS核心集被引频次:

SCOPUS被引频次: 9

ESI高被引论文在榜: 0 展开所有

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