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Title: A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions (English)
Author: Baltaev, Jamol I.
Author: Kučera, Milan
Author: Väth, Martin
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 57
Issue: 2
Year: 2012
Pages: 143-165
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: reaction-diffusion system
Keyword: unilateral condition
Keyword: variational inequality
Keyword: local bifurcation
Keyword: variational approach
Keyword: spatial patterns
MSC: 35B32
MSC: 35J50
MSC: 35J57
MSC: 35J87
MSC: 35J88
MSC: 35K57
MSC: 47J20
idZBL: Zbl 1249.35020
idMR: MR2899729
DOI: 10.1007/s10492-012-0010-2
Date available: 2012-03-05T07:03:21Z
Last updated: 2020-07-02
Stable URL:
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