Extinction Properties For Some Non-Newtonian Polytropic Filtration Equations With Singular Potentials

The nonlinear parabolic equations can be used to describe lots of diffusion phenomena that occur in nature,such as,heat conduction,combustion phenomena,population dispersal,etc.Various nonlinear mechanisms lead to the occurrence of the singularity of the solutions,such as,extinction in finite time.This thesis focuses on the global existence and extinction properties of the solutions of two classes of non-Newtonian polytropic filtration equations with singular potentials.Firstly,using the integral norm estimation approach and a series of inequalities,we prove that for any nonnegative initial value,the solution of the problem is global.Secondly,we give the sufficient conditions for the extinction phenomena of the solutions by using the energy estimation method,Sobolev inequality and some ordinary differential inequalities.Finally,by defining suitable energy functional,and using the upper and lower solution methods,we discuss the non-extinction of the solutions.