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, $u_t = J*u-u+ u^αv^p$, $v_t =Δv^+u^qv^β$, $p, q, α, β>0$ with homogeneous Dirichlet boundary conditions and positive initial data. We also give the blow-up rates for non-simultaneous blow-up.

Theorems & Definitions (19)

• Theorem 1.1
• Theorem 1.2
• Lemma 2.1
• proof
• Lemma 3.1
• proof
• Lemma 3.2
• proof
• Lemma 4.1
• proof