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 {ut=Δu+ur(x,t)∫Ωvs(x,t)dxinΩ×(0,t∗),vt=Δv+vq(x,t)∫Ωup(x,t)dxinΩ×(0,t∗) subject to u(x,t)=v(x,t)=0u(x,t)=v(x,t)=0 on ∂Ω×(0,t∗)∂Ω×(0,t∗) and nonnegative initial data under certain assumptions. Here Ω⊂RnΩ⊂Rn is a smooth bounded open domain and n≥3n≥3.