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作者:

Fengt, Yue-hong (Fengt, Yue-hong.) | Hu, Haifeng (Hu, Haifeng.) | Mein, Ming (Mein, Ming.) | Tsogtgerel, Gantumur (Tsogtgerel, Gantumur.) | Zhangii, Guojing (Zhangii, Guojing.)

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EI Scopus SCIE

摘要:

This paper is concerned with the relaxation-time limits to a multidimensional radial steady hydrodynamic model of semiconductors in the form of Euler-Poisson equations with sonic or nonsonic boundary as the relaxation time \tau \rightarrow \infty and \tau \rightarrow 0+, respectively, where the sonic boundary is the critical and difficult case, because of the degeneracy at the boundary and the formation of boundary layers. For the case of \tau \rightarrow \infty , after showing the boundedness of the density by using the divergence form, we prove the convergence of the solutions to their nontrivial asymptotic states with the convergence order O(\tau - 2 ) in the Lo degrees-sense. In order to overcome the degeneracy caused by the critical sonic boundary, we introduce an inverse transform as a technical tool to remove the secondorder degeneracy, and observe the advantage of a first-order degeneracy due to the monotonicity of this transformation. Moreover, when \tau \rightarrow 0+ with different boundary values, where the boundary layers appear, we show the strong convergence order O(\tau ) or O(\tau 1-\varepsilon ) for different boundary cases. In order to overcome the difficulty caused by the boundary layer, we propose a new technique in asymptotic limit analysis and identify the width of the boundary layers as O(\tau ). These new proposed methods develop and improve upon the existing studies. Finally, a series of numerical simulations are conducted, which corroborate our theoretical analysis, particularly regarding the formation of boundary layers.

关键词:

sonic boundary relaxation time limit multidimensional Euler--Poisson equations interior subsonic solu- tions

作者机构:

  • [ 1 ] [Fengt, Yue-hong]Beijing Univ Technol, Sch Math Stat & Mech, Beijing, Peoples R China
  • [ 2 ] [Hu, Haifeng]Changchun Univ, Sch Math & Stat, Changchun 130022, Peoples R China
  • [ 3 ] [Mein, Ming]Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China
  • [ 4 ] [Mein, Ming]Champlain Coll St Lambert, Dept Math, Quebec City, PQ J4P 3P2, Canada
  • [ 5 ] [Mein, Ming]McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada
  • [ 6 ] [Tsogtgerel, Gantumur]McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada
  • [ 7 ] [Mein, Ming]Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Peoples R China
  • [ 8 ] [Tsogtgerel, Gantumur]Natl Univ Mongolia, Dept Phys, Ulan Bator 14200, Mongolia

通讯作者信息:

  • [Hu, Haifeng]Changchun Univ, Sch Math & Stat, Changchun 130022, Peoples R China;;[Zhangii, Guojing]Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

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来源 :

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

ISSN: 0036-1410

年份: 2024

期: 5

卷: 56

页码: 6933-6962

2 . 0 0 0

JCR@2022

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