About: Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We consider a reaction–diffusion system of activator–inhibitor or substrate-depletion type which is subject to diffusion-driven instability if supplemented by pure Neumann boundary conditions. We show by a degree-theoretic approach that an obstacle (e.g. a unilateral membrane) modeled in terms of inequalities, introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable. Moreover, this parameter domain is rather different from the known case when also Dirichlet conditions are assumed. In particular, bifurcation arises for fast diffusion of activator and slow diffusion of inhibitor which is the difference from all situations which we know. We consider a reaction–diffusion system of activator–inhibitor or substrate-depletion type which is subject to diffusion-driven instability if supplemented by pure Neumann boundary conditions. We show by a degree-theoretic approach that an obstacle (e.g. a unilateral membrane) modeled in terms of inequalities, introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable. Moreover, this parameter domain is rather different from the known case when also Dirichlet conditions are assumed. In particular, bifurcation arises for fast diffusion of activator and slow diffusion of inhibitor which is the difference from all situations which we know. (en)
Title	Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions (en)
skos:prefLabel	Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions (en)
skos:notation	RIV/67985840:_____/12:00374182!RIV12-AV0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190805), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Kučera, Milan Väth, Martin
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	124921
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/12:00374182
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	global bifurcation; degree; stationary solutions (en)
http://linked.open.../riv/klicoveSlovo	degree global bifurcation stationary solutions
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[AF495F4A4FF1]
http://linked.open...i/riv/nazevZdroje	Journal of Differential Equations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Bifurcation and parameter dependence for unilateral boundary value problems and interpretation in natural sciences
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	252
http://linked.open...iv/tvurceVysledku	Väth, Martin Kučera, Milan
http://linked.open...ain/vavai/riv/wos	000300077400001
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0022-0396
number of pages	32 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jde.2011.10.016

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