Simultaneous and non-simultaneous blow-up criteria of solutions for a diffusion system with weighted localized sources

Abstract

This paper considers the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term, which is a product of localized source, local source, weight function, and complemented by homogeneous Dirichlet boundary conditions. It is proved that there exists initial data such that simultaneous or non-simultaneous blow-up occur. Moreover, the related classifications for the four parameters in the model is optimal and complete. The results extend those in Zhang and Yang (J. Appl. Math. Comput. 32:429–441, 2010).