This paper investigates 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, and weight function, and complemented by homogeneous Dirichlet boundary conditions. The criteria are proposed to identify simultaneous and nonsimultaneous blow-up solutions. Moreover, the related classification for the four parameters in the model is optimal and complete. The results extend those in Zhang and Yang [12].
