Stability of  stationary waves for full Euler-Poisson system  in multi-dimensional space

Ming Mei; Yong Wang

doi:10.3934/cpaa.2012.11.1775

Article Contents

2012, Volume 11, Issue 5: 1775-1807. Doi: 10.3934/cpaa.2012.11.1775

This issue Previous Article Instability of coupled systems with delay Next Article On the Lagrangian averaged Euler equations: local well-posedness and blow-up criterion

Stability of stationary waves for full Euler-Poisson system in multi-dimensional space

Ming Mei^1, and
Yong Wang^2,

1.
Department of Mathematics, Champlain College Saint-Lambert, Quebec, J4P 3P2
2.
Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100190

Received: February 2011

Revised: November 2011

Published: September 2012

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Abstract

This paper is concerned with the nonisentropic unipolar hydrodynamic model of semiconductors in the form of multi-dimensional full Euler-Poisson system. By heuristically analyzing the exact gaps between the original solutions and the stationary waves at far fields, we ingeniously construct some correction functions to delete these gaps, and then prove the $L^\infty$-stability of stationary waves with an exponential decay rate in 1-D case. Furthermore, based on the 1-D convergence result, we show the stability of planar stationary waves with also some exponential decay rate in $m$-D case.

Keywords:

Euler-Poisson system,
nonisentropic unipolar hydrodynamic model,
semiconductor devices,
stationary waves,
stability,
convergence rates.

Mathematics Subject Classification: Primary: 35L50, 35L60, 35L65; Secondary: 76R50.

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