Spatial patterns for reaction-diffusion systems with conditions described by inclusions
type: Item
instance of: scholarly article
title: Spatial patterns for reaction-diffusion systems with conditions described by inclusions
zbMATH Open document ID: 0940.35030
DOI: 10.1023/A:1022203129542
author: Jan Eisner
author: Milan Kučera
published in: Applications of Mathematics
publication date: 2000-05-22T00:00:00Z
full work available at URL: https://eudml.org/doc/32991
review text: A reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions is considered. The main result exhibits a destabilizing effect of these boundary conditions in the following sense. It is proved that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35K85
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 35J85
zbMATH DE Number: 1450135
zbMATH Keywords: destabilizing effect
zbMATH Keywords: variational inequalities inclusions
zbMATH Keywords: stationary solutions
MaRDI profile type: Publication
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OpenAlex ID: W10335988
description: scientific article; zbMATH DE number 1450135