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

0374182 - MÚ 2012 RIV US eng J - Článek v odborném periodiku
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
Grant CEP: GA AV ČR IAA100190805
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: global bifurcation * degree * stationary solutions
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.480, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0207157