Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up

Abstract

We study the possibility of defining a nontrivial continuation after the blow-up time for a system of two heat equations with a nonlinear coupling at the boundary. It turns out that any possible continuation that verify a maximum principle is identically infinity after the blow-up time, that is, both components blow up completely. We also analyze the propagation of the singularity to the whole space, the avalanche, when blow-up is non-simultaneous.