Global existence and blowup solutions for the Gierer-Meinhardt system
type: Item
instance of: scholarly article
title: Global existence and blowup solutions for the Gierer-Meinhardt system
zbMATH Open document ID: 1439.35263
author: Shaohua Chen
author: Brittney Melnick
author: Runzhang Xu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2020-04-23T00:00:00Z
review text: This article discusses the study of the Gierer-Meinhardt system in the form \[ \begin{cases} u_t=\Delta u-u+\frac{u^p}{v^q} &\quad x\in \Omega, t>0\\ v_t=\Delta v-\frac{v}{R}+\frac{u^r}{Rv^s} &\quad x\in \Omega, t>0\\ \frac{\partial u}{\partial n}=\frac{\partial v}{\partial n}=0&\quad x\in \partial \Omega, t>0\\ u(x,0)=u_0(x)>0, v(x,0)=v_0(x)>0 &\quad x\in \Omega, \end{cases} \] where \(\Omega\) is asmooth and bounded domain in \({\mathbb R}^N\), \(p>1\), \(q,r,s>0\). There are three main results in the article which present new sufficient conditions for global existence and finite time blow-up of solutions.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 7192512
zbMATH Keywords: global existence
zbMATH Keywords: blowup solutions
zbMATH Keywords: Gierer-Meinhardt systems
MaRDI profile type: Publication
full work available at URL: j.na.2020.111785
OpenAlex ID: W3004596705
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DOI: 10.1016/J.NA.2020.111785
description: scientific article; zbMATH DE number 7192512