Non-simultaneous blow-up for a system with local and non-local diffusion

TL;DR

This paper investigates conditions under which solutions to a coupled semilinear PDE system blow up at different times, analyzing non-simultaneous blow-up phenomena and their rates for systems with local and non-local diffusion.

Contribution

It introduces new results on non-simultaneous blow-up in coupled PDE systems with local and non-local diffusion, including blow-up rate estimates.

Findings

Non-simultaneous blow-up can occur under certain conditions.

Explicit blow-up rate formulas are derived.

The study extends understanding of blow-up behavior in coupled PDEs.

Abstract

We study the possibility of non-simultaneous blow-up for positive solutions of a coupled system of two semilinear equations, $u_t = J*u-u+ u^\alpha v^p$, $v_t =\Delta v^+u^qv^\beta$, $p, q, \alpha, \beta>0$ with homogeneous Dirichlet boundary conditions and positive initial data. We also give the blow-up rates for non-simultaneous blow-up.