Asymptotic convergence to planar stationary waves for multi-dimensional unipolar hydrodynamic model of semiconductors

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Huang, Feimin¹  Mei, Ming^2,3  Wang, Yong¹  Yu, Huimin⁴ 

[1] Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China

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

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

[4] Shandong Normal Univ, Dept Math, Jinan 250014, Peoples R China

关键词: Euler-Poisson equations;    Unipolar hydrodynamic model of semiconductor;    Nonlinear damping;    Planar stationary waves;    Asymptotic convergence;    Exponential decay rates;   

DOI  :  10.1016/j.jde.2011.04.007

来源: Elsevier

【 摘 要 】

In this study, we consider the high dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations. Based on the results that we have obtained in the first part (Huang, et al., 2011 [16]) for the 1-D case, we can further show the stability of planar stationary waves in multi-dimensional case. Utilizing the energy method, we obtain the global existence of the solutions of high dimensional Euler-Poisson equations for the unipolar hydrodynamic model, and prove that the solutions converge to the planar stationary waves time-exponentially. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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