Title: A variational approach to bifurcation points of a reaction-diffusion system with obstacles and neumann boundary conditions
Authors: Eisner, Jan
Kučera, Milan
Väth, Martin
Citation: Applications of Mathematics, 2016, roč. 61, č. 1, s. 1-25. ISSN 0862-7940.
Issue Date: 2016
Publisher: Akademie věd České republiky
Technical University of Liberec
Document type: článek
URI: http://hdl.handle.net/11025/25672
ISSN: 0862-7940
Keywords: reakčně-difúzní systém;jednostranný stav;variační nerovnost;místní rozdvojení;variační přístup;prostorové vzory;Turingova nestabilita
Keywords in different language: reaction-diffusion system;unilateral condition;variational inequality;local bifurcation;variational approach;spatial patterns;Turing instability
Abstract in different language: 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.
Rights: © Akademie věd České republiky
Plný text je přístupný v rámci univerzity přihlášeným uživatelům.
Appears in Collections:Články / Articles (KMA)

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