Structure of solutions to a singular Liouville system arising from modeling dissipative stationary plasmas
type: Item
instance of: scholarly article
title: Structure of solutions to a singular Liouville system arising from modeling dissipative stationary plasmas
zbMATH Open document ID: 1295.35217
author: Jann-Long Chern
author: Zhiyou Chen
author: Yong-Li Tang
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-04-24T00:00:00Z
review text: \quad In this paper, the authors study a system of elliptic equations which arises from modeling dissipative stationary plasmas. More precisely, denote by \(B_R\) the ball of radius \(R>0\) in \(\mathbf{R}^2\), then the system takes the form \[ \;\;\;\;\left\{\begin{align*}{ &\Delta u+a e^u+ b e^v=4\pi k_1 \delta_0,\;\;x\in B_R, \cr &\Delta v+c e^u+ d e^v=4\pi k_2 \delta_0,\;\;x\in B_R,\cr & u<0,\;v<0\;\;\text{ in }\; B_R,\;\;\cr & u=v=0\;\;\text{ on }\; \partial B_R, }\end{align*}\right. \] where \(a,d\leq 0\), \(b,c>0\), \(k_1,k_2>0\) are constants and where \(\delta_0\) is the Dirac measure at the origin. \vskip 3 mm \quad With some assumptions on the parameters \(a,b,c,d\), the authors obtain existence and uniqueness results for radial solutions, and study blow up phenomena.
reviewed by: Laurent Thomann
Mathematics Subject Classification ID: 35J47
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35Q82
Mathematics Subject Classification ID: 82D10
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6157305
zbMATH Keywords: Liouville system
zbMATH Keywords: structure of solutions
zbMATH Keywords: dissipative stationary plasma
MaRDI profile type: Publication
full work available at URL: dcds.2013.33.2299
OpenAlex ID: W2334076392
DOI: 10.3934/DCDS.2013.33.2299
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description: scientific article; zbMATH DE number 6157305