Abstract

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.

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