Bifurcation for a reaction-diffusion system with unilateral obstacles with pointwise and integral conditions

0353059 - MÚ 2011 RIV GB eng J - Journal Article
Väth, Martin
Bifurcation for a reaction-diffusion system with unilateral obstacles with pointwise and integral conditions.
Nonlinear Analysis: Real World Applications. Roč. 12, č. 2 (2011), s. 817-836. ISSN 1468-1218. E-ISSN 1878-5719
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: 2.043, year: 2011
http://www.sciencedirect.com/science/article/pii/S1468121810001951

A reaction-diffusion system of activator-inhibitor or substrate-depletion type is considered which is subject to diffusion driven instability. It is shown that obstacles (e.g. a unilateral membrane) for one or both quantities introduce a new bifurcation of spatially non-homogeneous steady states in a parameter domain where the trivial branch is exponentially stable without obstacles. The obstacles are modeled in terms of inclusions. Moreover, simultaneously some of the obstacles can be modeled also using nonlocal integral conditions.
Permanent Link: http://hdl.handle.net/11104/0192405