A Note on Diffusion-Induced Blow-up

The goal of paper is to give a simpler proof and some extensions of a result of Weinberger 3] concerning diffusion induced blow-up. The result states that, for certain systems of two parabolic equations with equal diffusion and homogeneous Neumann boundary conditions, some blowing-up solutions exist, although the corresponding system of ODE’s has only global bounded solutions. To Professor Pavol Brunovsky, on the occasion of his 70th birthday.