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

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