Boundary Layer Problem and Quasineutral Limit of Compressible Euler-Poisson System

Shu Wang; Chundi Liu

doi:10.3934/cpaa.2017108

Article Contents

2017, Volume 16, Issue 6: 2177-2199. Doi: 10.3934/cpaa.2017108

This issue Previous Article Multiple positive solutions for Kirchhoff type problems involving concave-convex nonlinearities Next Article Existence and convexity of solutions of the fractional heat equation

Boundary Layer Problem and Quasineutral Limit of Compressible Euler-Poisson System

Shu Wang and
Chundi Liu^,

College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China

* Corresponding author
* Corresponding author

Received: December 31, 2016

Revised: February 28, 2017

Published: September 2017

Shu Wang is supported by NSF grant 11371042, Chundi Liu is supported by NSF grant 11471028,11601021

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We study the boundary layer problem and the quasineutral limit of the compressible Euler-Poisson system arising from plasma physics in a domain with boundary. The quasineutral regime is the incompressible Euler equations. Compared to the quasineutral limit of compressible Euler-Poisson equations in whole space or periodic domain, the key difficulty here is to deal with the singularity caused by the boundary layer. The proof of the result is based on a λ-weighted energy method and the matched asymptotic expansion method.

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Mathematics Subject Classification: Primary: 35B25, 35B40; Secondary: 35K57.

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