Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions

0374182 - MÚ 2012 RIV US eng J - Journal Article
Kučera, Milan - Väth, Martin
Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions.
Journal of Differential Equations. Roč. 252, č. 4 (2012), s. 2951-2982. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA AV ČR IAA100190805
Institutional research plan: CEZ:AV0Z10190503
Keywords : global bifurcation * degree * stationary solutions
Subject RIV: BA - General Mathematics
Impact factor: 1.480, year: 2012
http://www.sciencedirect.com/science/article/pii/S0022039611004530

We consider a reaction–diffusion system of activator–inhibitor or substrate-depletion type which is subject to diffusion-driven instability if supplemented by pure Neumann boundary conditions. We show by a degree-theoretic approach that an obstacle (e.g. a unilateral membrane) modeled in terms of inequalities, introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable. Moreover, this parameter domain is rather different from the known case when also Dirichlet conditions are assumed. In particular, bifurcation arises for fast diffusion of activator and slow diffusion of inhibitor which is the difference from all situations which we know.
Permanent Link: http://hdl.handle.net/11104/0207157