Study On The Dynamic Properties Of Solutions Of Two Kinds Of Parabolic Equations With Logarithmic Nonlinearity

In this dissertation,the potential well theory,energy estimation and differential inequality are used to study the dynamic properties of solutions of two kinds of Parabolic Equations with logarithmic nonlinearity in proper Sobolev space,such as the well-posedness,global existence conditions and blow up conditions and so on.This paper is divided into three chapters.The first chapter mainly introduces the research object,background,purpose,method and innovation.In Chapter 2,we study the dynamic properties of solutions for a class of Semi-linear heat equations with logarithmic nonlinearity under the boundary conditions of bounded region ?(?)Rn with homogeneous Dirichlet boundary condition.By using the potential well method,the contradiction method,and the concave method,the global existence and finite time blow up of the solution of the equation are discussed in Sobolev space H01(?)and the upper bound of blow up time is estimated.In Chapter 3,under the boundary conditions of bounded region ?(?)Rn and homogeneous Dirichlet boundary condition,where 0<s<1,the dynam-ic properties of solutions of a class of Semi-linear Parabolic Equations with log-arithmic nonlinear terms and fractional order Laplace operators(-?)s are stud-ied.Using the similar method in Chapter 2,the global existence and finite time blow up of the solution of the equation are discussed in fractional Sobolev space X0(?)={u?Hs(Rn):u(x)=0 a.e.x?Rn\?} and the upper bound of blow up time is estimated.