Total versus single point blow-up in heat equations with coupled localized sources

Abstract

This paper considers heat equations with local and coupled localized sources subject to null Dirichlet boundary conditions. The behavior of solutions depends on the interactions among the local and localized sources as well as the diffusions with the null boundary conditions in the model. The aim of the paper is to distinguish total and single point blow-up for the non-global solutions. In addition, simultaneous versus non-simultaneous blow-up of solutions under different dominations are determined also with four possible simultaneous blow-up rates.