Communications in Mathematical Sciences

Volume 10 (2012)

Number 2

Transonic shock solutions for a system of Euler-Poisson equations

Pages: 419 – 462

DOI: https://dx.doi.org/10.4310/CMS.2012.v10.n2.a1

Authors

Tao Luo (Department of Mathematics and Statistics, Georgetown University, Washington)

Zhouping Xin (Institute of Mathematical Sciences, The Chinese University of Hong Kong)

Abstract

A boundary value problem for a system of Euler-Poisson equations modeling semiconductor devices or plasma is considered. The boundary conditions are supersonic inflow and subsonic outflow. The purpose of this paper is to elucidate the role played by the electric field in the structure of solutions with transonic shocks. The existence, non-existence, uniqueness, and non-uniqueness of solutions with transonic shocks are obtained according to the different cases of boundary data and physical interval length. Detailed structures of solutions are given. Shock locations are determined by the boundary data. Different phenomena are shown for the different situations when the density of fixed, positively charged background ions is in supersonic and subsonic regimes.

Keywords

Euler-Poisson equations, transonic shocks

2010 Mathematics Subject Classification

35L65, 35L67, 35Q35

Published 21 December 2011