Lower bounds estimate for the blow-up time of a nonlinear nonlocal porous medium equation

The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equationut=Δum+up∫Ωuqdxut=Δum+up∫Ωuqdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condition is given in this article by using a differential inequality technique.