# American Institute of Mathematical Sciences

July  2011, 16(1): 345-360. doi: 10.3934/dcdsb.2011.16.345

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

 1 Department of Mathematics, Shanghai Normal University, Shanghai 200234

Received  February 2009 Revised  January 2011 Published  April 2011

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.
Citation: Yeping Li. Existence and some limit analysis of stationary solutions for a multi-dimensional bipolar Euler-Poisson system. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 345-360. doi: 10.3934/dcdsb.2011.16.345
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