Blow up Property of the Solution for Quasi Linear Parabolic Equations and Its Application

This dissertation is to discuss the initial-boundary value problem under the third nonlinear boundary condition for a kindof quasi-linear parabolic equations. To apply the maximum value theory and convex method, it is proved that the blowingup of solution in the definite time. And for application, this paper research into a mathematics model of fluids in porousmedium. And have got the blowing up behavior for the problem in limited time.