Bifurcation points of reaction-diffusion systems with unilateral conditions
Pavel Drábek, Milan Kučera, Marta Míková (1985)
Czechoslovak Mathematical Journal
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Pavel Drábek, Milan Kučera, Marta Míková (1985)
Czechoslovak Mathematical Journal
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Eisner, Jan (2000)
Mathematica Bohemica
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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...
Jan Eisner, Milan Kučera (1997)
Applications of Mathematics
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We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded. ...