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On uniqueness and monotonicity of solutions of non-local reaction diffusion equation

Abstract : This article deals with the uniqueness and the behavior of solutions of non-local reaction diffusion equations. Since these equations share many properties with the usual reaction diffusion model, such as a form of maximum principle and the translation invariance, uniqueness and monotone behavior for the solution, as in the usual case, are expected. I present an elementary proof of this monotone behavior. The proof essentially uses techniques based on the maximum principle and the sliding method
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Submitted on : Saturday, May 30, 2020 - 7:18:26 PM
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Jerome Coville. On uniqueness and monotonicity of solutions of non-local reaction diffusion equation. Annali di Matematica Pura ed Applicata, Springer Verlag, 2006, 185 (3), pp.461-485. ⟨10.1007/s10231-005-0163-7⟩. ⟨hal-02659813⟩

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