Radial solutions of hydrodynamic model of semiconductors with sonic boundary

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:501

Article

Chen, Liang¹  Mei, Ming^2,3  Zhang, Guojing¹  Zhang, Kaijun¹ 

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Champlain Coll St Lambert, Dept Math, St Lambert, PQ J4P 3P2, Canada

[3] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

关键词: Euler-Poisson equations;    Sonic boundary;    Radial subsonic solution;    Radial supersonic solution;    Hydrodynamic model of semiconductors;   

DOI  :  10.1016/j.jmaa.2021.125187

来源: Elsevier

【 摘 要 】

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 the n-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 twosteps iteration scheme to build up the key energy estimates. This is the first attempt to study the n-D steady-states with the sonic boundary, and the results obtained essentially improve and develop the previous studies in the one-dimensional case. (c) 2021 Published by Elsevier Inc.

【 授权许可】

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