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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 ASEP0458817
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleA 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
    Source TitleApplications of Mathematics. - : Matematický ústav AV ČR, v. v. i. - ISSN 0862-7940
    Roč. 61, č. 1 (2016), s. 1-25
    Number of pages25 s.
    Publication formPrint - P
    Languageeng - English
    CountryCZ - Czech Republic
    Keywordsreaction-diffusion system ; unlateral condition ; variational inequality
    Subject RIVEG - Zoology
    Subject RIV - cooperationMathematical Institute - General Mathematics
    R&D ProjectsGA13-12580S GA ČR - Czech Science Foundation (CSF)
    Institutional supportUZFG-Y - RVO:67985904 ; MU-W - RVO:67985840
    UT WOS000369303200001
    EID SCOPUS84957589965
    DOI10.1007/s10492-016-0119-9
    AnnotationGiven 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.
    WorkplaceInstitute of Animal Physiology and Genetics
    ContactJana Zásmětová, knihovna@iapg.cas.cz, Tel.: 315 639 554
    Year of Publishing2017