A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions

0376831 - MÚ 2013 RIV CZ eng J - Journal Article
Baltaev, J.I. - Kučera, Milan - Väth, Martin
A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions.
Applications of Mathematics. Roč. 57, č. 2 (2012), s. 143-165. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA AV ČR IAA100190805
Institutional research plan: CEZ:AV0Z10190503
Keywords : reaction-diffusion system * unilateral condition * variational inequality
Subject RIV: BA - General Mathematics
Impact factor: 0.222, year: 2012
http://www.springerlink.com/content/e1km86727356pl88/

We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential operator, and a variational approach is used in a certain non-direct way.
Permanent Link: http://hdl.handle.net/11104/0209139