. "0022-0396" . "V\u00E4th, Martin" . "124921" . . "Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions" . . "2"^^ . "We consider a reaction\u2013diffusion system of activator\u2013inhibitor 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." . "2"^^ . "V\u00E4th, Martin" . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions"@en . . "We consider a reaction\u2013diffusion system of activator\u2013inhibitor 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 . . . . "Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions" . "32"^^ . . "10.1016/j.jde.2011.10.016" . "[AF495F4A4FF1]" . "000300077400001" . . . "P(IAA100190805), Z(AV0Z10190503)" . "global bifurcation; degree; stationary solutions"@en . "Journal of Differential Equations" . "4" . "252" . "RIV/67985840:_____/12:00374182!RIV12-AV0-67985840" . "RIV/67985840:_____/12:00374182" . "Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions"@en . "Ku\u010Dera, Milan" . . . . . . . .