Dynamical Properties Of Two Kinds Of Nonlinear Evolution Equations With Singular Potential

By using the techniques of potential well method,ordinary differential inequal-ities and energy estimation,this paper studies the well-posedness of two kinds of nonlinear evolutions with singular potential in Sobolev space and Lebesgue space,and analyzes the dynamic properties of the solution,such as global existence,infinite time blow-up and finite time extinction.In the first chapter,the research background and existing results of two kinds of nonlinear evolution equations with singular potential discussed in this paper are introduced,and on this basis,the research purpose of this paper is introduced.In the second chapter,we study a class of semilinear heat equations with sin-gular potential and logarithmic nonlinearity.Firstly,by using logarithmic Sobolev inequality and Faedo-Galerkin method,we establish the local well-posedness of the solution of the equation.Secondly,by using the potential well method,we analyze the global existence and infinite time blow-up conditions of the solution.In the third chapter,we study a class of fast diffusion p-Laplace equations with singular potential.By using energy estimation,Hardy-Littlewood-Sobolev inequal-ity and some ordinary differential inequalities,we obtain the global existence of the solution of the equation and analyze the extinction and non-extinction conditions of the global solution.