Bifurcation points for a reaction–diffusion system with two inequalities☆

https://doi.org/10.1016/j.jmaa.2009.10.037Get rights and content
Under an Elsevier user license
open archive

Abstract

We consider a reaction–diffusion system of activator-inhibitor or substrate-depletion type which is subject to diffusion-driven instability. We show that obstacles (e.g. a unilateral membrane) for both quantities modeled in terms of inequalities introduce a new bifurcation of spatially non-homogeneous steady states in the domain of stability of the trivial solution of the corresponding classical problem without obstacles.

Keywords

Global bifurcation
Degree
Stationary solutions
Reaction–diffusion system
Variational inequality
Inclusion
Signorini boundary condition
Laplace operator

Cited by (0)

☆

The first two authors are supported by the Academy of Sciences of the Czech Republic under the Grant IAA100190805 of the GAAV and the Institutional Research Plan AV0Z10190503. The third author is a Heisenberg fellow (Az. VA 206/1-1 and VA 206/1-2). Financial support by the DFG is gratefully acknowledged.

1

Current address: Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, Czech Republic.

Copyright © 2009 Elsevier Inc. All rights reserved.