Article
MSC:
35B32,
35J50,
35J57,
35J87,
35J88,
35K57,
47J20 | MR 2899729 | Zbl 1249.35020 | DOI: 10.1007/s10492-012-0010-2
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Keywords:
reaction-diffusion system; unilateral condition; variational inequality; local bifurcation; variational approach; spatial patterns
reaction-diffusion system; unilateral condition; variational inequality; local bifurcation; variational approach; spatial patterns
Summary:
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 a potential operator, and a variational approach is used in a certain non-direct way.
References:
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