Existence and some limit analysis of stationary solutions for amulti-dimensional bipolar Euler-Poisson system

Yeping Li

doi:10.3934/dcdsb.2011.16.345

Article Contents

2011, Volume 16, Issue 1: 345-360. Doi: 10.3934/dcdsb.2011.16.345

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Existence and some limit analysis of stationary solutions for a multi-dimensional bipolar Euler-Poisson system

Yeping Li^1,

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234

Received: January 31, 2009

Revised: December 31, 2010

Published: June 2011

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Abstract

In this paper, we study a two- and three-dimensional bipolar Euler-Poisson system (hydrodynamic model). The system arises in mathematical modeling for semiconductors and plasmas. We are interested in the steady state isentropic case supplemented by the proper boundary conditions. We first show the existence and uniqueness of irrotational subsonic stationary solutions for the two- and three-dimensional hydrodynamic model. Next, we investigate the zero-electron-mass limit, the zero-relaxation-time limit and the Debye-length (quasi-neutral) limit for above stationary solutions, respectively. For each limit, we show the strong convergence of the sequence of solutions and give the associated convergence rates.

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Mathematics Subject Classification: Primary: 35B40, 70K75, 74G55, 76M45.

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