Article
MSC:
35B32,
35J85,
35K57,
35K58,
35K85,
47H04,
47H15,
47N20 | MR 1475051 | Zbl 0940.35030 | DOI: 10.1023/A:1022203129542
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Keywords:
reaction-diffusion systems; variational inequalities; inclusions; bifurcation; stationary solutions; spatial patterns
reaction-diffusion systems; variational inequalities; inclusions; bifurcation; stationary solutions; spatial patterns
Summary:
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.
References:
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