Existence and stability of multiple-spot solutions for the Gray-Scott model in \(\mathbb{R}^2\)
type: Item
instance of: scholarly article
title: Existence and stability of multiple-spot solutions for the Gray-Scott model in \(\mathbb{R}^2\)
zbMATH Open document ID: 1014.37036
DOI: 10.1016/S0167-2789(02)00743-1
author: Matthias Winter
author: Juncheng Wei
published in: Physica D
publication date: 2003-02-11T00:00:00Z
review text: In the present paper, the authors study the Gray-Scott model in a bounded domain \(\Omega\subset \mathbb{R}^2\). First they rigorously construct multiple interior spot solutions and then they prove results on the stability of such solutions. To this end the authors essentially use the Green function and its derivatives together with two nonlocal eigenvalue problems. Moreover they present a threshold behaviour for the stability.
Mathematics Subject Classification ID: 37J25
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K50
zbMATH DE Number: 1867614
zbMATH Keywords: Green function
zbMATH Keywords: nonlocal eigenvalue problems
zbMATH Keywords: threshold behavior
zbMATH Keywords: multiple interior spot solutions
zbMATH Keywords: stability
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: s0167-2789(02)00743-1
OpenAlex ID: W2002181677
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description: scientific article; zbMATH DE number 1867614