Diffusion-driven blow-up for a non-local Fisher-KPP type model
Analysis of PDEs
2020-07-17 v2
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.
Keywords
Cite
@article{arxiv.1905.05495,
title = {Diffusion-driven blow-up for a non-local Fisher-KPP type model},
author = {Nikos I. Kavallaris and Evangelos A. Latos},
journal= {arXiv preprint arXiv:1905.05495},
year = {2020}
}