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Bifurcation points of reaction-diffusion systems with unilateral conditions. (English) Zbl 0604.35042
Stationary solutions of reaction-diffusion systems with unilateral conditions are considered. The problem is formulated in terms of abstract inequalities on cones in a Hilbert space. The diffusion coefficient plays the role of a bifurcation parameter. It is proved that there exists a bifurcation point lying in the domain of parameters for which a spatially homogeneous stationary solution of the classical problem with suitable boundary conditions is stable. It follows from here that spatially nonhomogeneous stationary solutions of the reaction-diffusion system with unilateral conditions exist for some parameters for which the problem with the classical boundary conditions has only a spatially homogeneous stationary solution.

35K57 Reaction-diffusion equations
35B32 Bifurcations in context of PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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