Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions
Pavel Drábek, Milan Kučera (1986)
Czechoslovak Mathematical Journal
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Pavel Drábek, Milan Kučera (1986)
Czechoslovak Mathematical Journal
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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.
Kučera, Milan
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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. ...