| This thesis is mainly about the extinction properties of the solutions of two types of fast diffusion equations.Firstly,we study the extinction property of the solution to a class of fast diffusion equation with gradient source term and singular coefficient.By analyzing the effects of the singular coefficient,gradient source and fast diffusion term on the extinction property of the solution,using energy method and upper and lower solution methods,we give the sufficient conditions on the occurrence of the extinction singularity of the solution,and prove the non-extinction result.Secondly,we discuss the extinction properties of the solutions to a kind of quasilinear parabolic equations with nonlinear nonlocal source,we give the critical extinction exponent of the solution and the decay estimate of the extinction solution. |
