Asymptotic behavior of solutions to Euler-Poisson equations for bipolar hydrodynamic model of semiconductors

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Donatelli, Donatella¹  Mei, Ming^2,3  Rubino, Bruno¹  Sampalmieri, Rosella¹ 

[1] Univ Aquila, Dept Informat Engn Comp Sci & Math, I-67100 Laquila, Italy

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

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

关键词: Euler-Poisson equations;    Bipolar hydrodynamic model;    Stationary solutions;    Asymptotic behavior;    Convergence rates;   

DOI  :  10.1016/j.jde.2013.07.027

来源: Elsevier

【 摘 要 】

In this paper we study the Cauchy problem for 1-D Euler-Poisson system, which represents a physically relevant hydrodynamic model but also a challenging case for a bipolar semiconductor device by considering two different pressure functions and a non-flat doping profile. Different from the previous studies (Gasser et al., 2003 [7], Huang et al., 2011 [12], Huang et al., 2012 [13]) for the case with two identical pressure functions and zero doping profile, we realize that the asymptotic profiles of this more physical model are their corresponding stationary waves (steady-state solutions) rather than the diffusion waves. Furthermore, we prove that, when the flow is fully subsonic, by means of a technical energy method with some new development, the smooth solutions of the system are unique, exist globally and time-algebraically converge to the corresponding stationary solutions. The optimal algebraic convergence rates are obtained. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free