Global existence and blow-up for a nonlinear reaction-diffusion system

Abstract

We consider the nonlinear reaction-diffusion system ut - Δu = um1vn1, vt - Δv = um2vn2, subject to Dirichlet boundary conditions and m2 > m1 - 1, n1 > n2 - 1. We prove that if m1 ≤ 1, n2 ≤ 1, and m2n1 ≤ (1 - m1)(1 - n2) all nonnegative solutions are global, while if m1 > 1, or n2 > 1, or m2n1 > (1 - m1)(1 - n2) both global existence and finite time blow-up coexist. © 1997 Academic Press.