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A variational approach to bifurcation points of a reaction-diffusion system with obstacles and neumann boundary conditions
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SYSNO ASEP 0458817 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A variational approach to bifurcation points of a reaction-diffusion system with obstacles and neumann boundary conditions Author(s) Eisner, Jan (UZFG-Y)
Kučera, Milan (MU-W) RID, SAI, ORCID
Väth, Martin (MU-W) RID, SAI, ORCIDSource Title Applications of Mathematics. - : Springer - ISSN 0862-7940
Roč. 61, č. 1 (2016), s. 1-25Number of pages 25 s. Publication form Print - P Language eng - English Country CZ - Czech Republic Keywords reaction-diffusion system ; unlateral condition ; variational inequality Subject RIV EG - Zoology Subject RIV - cooperation Mathematical Institute - General Mathematics R&D Projects GA13-12580S GA ČR - Czech Science Foundation (CSF) Institutional support UZFG-Y - RVO:67985904 ; MU-W - RVO:67985840 UT WOS 000369303200001 EID SCOPUS 84957589965 DOI 10.1007/s10492-016-0119-9 Annotation Given a reaction-diffusion system which exhibits Turing's diffusion-driven instability, the influence of unilateral obstacles of opposite sign (source and sink) on bifurcation and critical points is studied. In particular, in some cases it is shown that spatially nonhomogeneous stationary solutions (spatial patterns) bifurcate from a basic spatially homogeneous steady state for an arbitrarily small ratio of diffusions of inhibitor and activator, while a sufficiently large ratio is necessary in the classical case without unilateral obstacles. The study is based on a variational approach to a non-variational problem which even after transformation to a variational one has an unusual structure for which usual variational methods do not apply. Workplace Institute of Animal Physiology and Genetics Contact Jana Zásmětová, knihovna@iapg.cas.cz, Tel.: 315 639 554 Year of Publishing 2017
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