A Lower Bound Of Blow-up Time For A Degenerate Diffusion Equation With Gradient Term

This paper deals with a degenerate nonlinear diffusion equation with gradient term, where q>1, p,r,s,μ>0with r+s≥1, Ω(?)R3is a bounded domain with smooth boundary, u0∈C0(Ω) with u0>0in Ω, and u0=0on (?)Ω.We at first determine finite time blow-up of solutions in some integral measure by the com-parison principle, and then estimate a lower bound of the blow-up time by using the differential inequality technique.