DIFFUSION-DRIVEN BLOW-UP FOR A NONLOCAL FISHER-KPP TYPE MODEL

The purpose of the current paper is to unveil the key mechanism which is responsible for the occurrence of Turing-type instability for a nonlocal Fisher-KPP model. In particular, we prove that the solution of the considered nonlocal Fisher-KPP equation in the neighborhood of a constant stationary solution is destabilized via a diffusion-driven blow-up. It is also shown that the observed diffusion-driven blow-up is complete, while its blow-up rate is completely classified. Finally, the detected 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.

Automated summary

The current paper aims to uncover the key mechanism behind the occurrence of Turing-type instability in a nonlocal Fisher-KPP model. It is demonstrated that the solution of the considered equation is destabilized near a constant stationary solution due to diffusion-driven blow-up. The complete blow-up of the observed diffusion-driven instability is classified in terms of its blow-up rate. Furthermore, the detected diffusion-driven instability leads to the formation of unstable blow-up patterns, which are identified by analyzing the blow-up profile of the solution.