Blow-up phenomena for a nonlinear reaction-diffusion system with time dependent coefficients

We investigate the blow-up phenomena for the solution to a nonlinear reaction-diffusion system with time dependent coefficients subject to null Dirichlet boundary conditions. By virtue of Kaplan's method, method of subsolutions and supersolutions and modified differential inequality technique, we establish the blow-up criteria for the solution. Moreover, lower and upper bounds for the blow-up time are derived.