Diffusion-driven blow-up for a non-local Fisher-KPP type model

2019/05/14 by Nikos I. Kavallaris, Kavallaris, Nikos I., Evangelos Latos +2 · 3 citations
Computer Science · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Stochastic processes and statistical mechanics #math.AP

paper · pdf · doi:10.48550/arxiv.1905.05495

openalex publication_date 2019/05/14 · arxiv created 2020/07/15 · arxiv updated 2020/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of the current paper is to unveil the key mechanism which is responsible for the occurrence of \it Turing-type instability for a non-local Fisher-KPP type model. In particular, we prove that the solution of the considered non-local Fisher-KPP equation in the neighbourhood of a constant stationary solution, is destabilized via a \it diffusion-driven blow-up. It is also shown that the observed \it diffusion-driven blow-up is complete, whilst its blow-up rate is completely classified. Finally, the detected \it diffusion-driven instability results in the formation of unstable blow-up patterns, which are also identified through the determination of the blow-up profile of the solution.

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