Lower Bounds For The Blow-up Time In A Nonlinear Diffusion Equation With Nonlinear Boundary Condition

This paper deals with the blow-up time of the nonlinear diffusion equation with nonlinear boundary conditions, where p, q>0. We assume that Ω(?)R3is a bounded domain with smooth boundary (?)Ω. assumed to be star-shaped and convex in two orthogonal directions, m>1,(?)um/(?)v denotes the outward normal derivative on the boundary.The necessary and sufficient conditions for the solution of the equation is max(p, q)>1. The lower bounds for the blow-up time are obtained by using a differential inequality technique. So we consider the problem in two cases. In Chapter3we assume that q>1,p>0, and estimate a lower bound of the blow up time in integral measure. In Chapter4we get lower bound of the blow up time in integral measure if p>1, q>0.