Bounds for the blowup time of the solution to a parabolic system with nonlocal factors in nonlinearities

In this paper, we establish the lower and upper bounds for the blow-up time of the solution to a system of parabolic equations { u t = Δ u + u r ( x , t ) ? ? v s ( x , t ) d x in ? × ( 0 , t ? ) , v t = Δ v + v q ( x , t ) ? ? u p ( x , t ) d x in ? × ( 0 , t ? ) subject to u ( x , t ) = v ( x , t ) = 0 on ? ? × ( 0 , t ? ) and nonnegative initial data under certain assumptions. Here ? ? R n is a smooth bounded open domain and n ? 3 .