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Instability of multi-spot patterns in shadow systems of reaction-diffusion equations. (English) Zbl 1312.35017

Summary: Our aim in this paper is to prove the instability of multi-spot patterns in a shadow system, which is obtained as a limiting system of a reaction-diffusion model as one of the diffusion coefficients goes to infinity. Instead of investigating each eigenfunction for a linearized operator, we characterize the eigenspace spanned by unstable eigenfunctions.

MSC:

35B36 Pattern formations in context of PDEs
35K57 Reaction-diffusion equations
37L15 Stability problems for infinite-dimensional dissipative dynamical systems
35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs
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