Bifurcation points for a reaction-diffusion system with two inequalities

0336125 - MÚ 2010 RIV US eng J - Journal Article
Eisner, J. - Kučera, Milan - Väth, M.
Bifurcation points for a reaction-diffusion system with two inequalities.
Journal of Mathematical Analysis and Applications. Roč. 365, č. 1 (2010), s. 176-194. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA AV ČR IAA100190805
Institutional research plan: CEZ:AV0Z10190503
Keywords : global bifurcation * degree * stationary solutions * reaction-diffusion system * variational inequality * Signorini boundary condition * Laplace operator
Subject RIV: BA - General Mathematics
Impact factor: 1.174, year: 2010
http://www.sciencedirect.com/science/article/pii/S0022247X09008579

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.
Permanent Link: http://hdl.handle.net/11104/0180430