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

Abstract

We study the possibility of non-simultaneous blow-up for positive solutions of a coupled system of two semilinear equations, ut = J ∗ u − u + uαv p, vt = v + uq vβ , p, q, α, β > 0 with homogeneous Dirichlet boundary conditions and positive initial data. We also give the blow-up rates for non-simultaneous blow-up.