Displaying similar documents to “Spatial patterns for reaction-diffusion systems with conditions described by inclusions”

A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions

Jamol I. Baltaev, Milan Kučera, Martin Väth (2012)

Applications of Mathematics

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We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with...

Destabilization for quasivariational inequalities of reaction-diffusion type

Vítězslav Babický (2000)

Applications of Mathematics

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We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.