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Instability of multi-spot patterns in shadow systems of reaction-diffusion equations

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  • 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.
    Mathematics Subject Classification: Primary: 35B36, 35K57; Secondary: 37L15.


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