Dynamic Properties Of Solutions To Two Types Of Nonlinear Plate Equations With Hardy-Hénon Potential Or Viscoelastic Term

In this thesis,we mainly study the dynamic properties of the solutions of two types of nonlinear plate equations with Hardy-Hénon potential or viscoelastic term,including the local well-posedness,the global existence,finite time blow-up and blow-up time estimate of the solutions.In the first part,we study the initial-boundary value problem of a class of nonlinear plate equations with Hardy-Hénon potential and polynomial nonlinear source terms.First,we establish the local well-posedness of the model solution by using the theory of operator semigroups.Next,after making some suitable assumptions on the Hardy-Hénon potential,we get the conditions on finite time blow-up of solutions with non-positive initial energy.Finally,we obtain the conditions on global existence and finite time blow-up of solutions with subcritical initial energy and critical initial energy.In the second part,we study the initial-boundary value problem of a class of nonlinear viscoelastic plate equations with polynomial nonlinear source terms.First,we establish the local well-posedness and energy equation of the model solution by using the Faedo-Gal(?)rkin method.Next,after making some suitable assumptions on the nonlinear viscoelastic plate equation,we get the conditions on global existence and finite time blow-up of solutions with non-positive initial energy and positive initial energy.The specific organization is as follows:In the first chapter,we introduce the related research background of the nonlinear plate equation with Hardy-Hénon potential and viscoelastic term,the research purpose and the symbols used in this thesis.In the second chapter,we study the initial-boundary value problem of a class of nonlinear plate equations with Hardy-Hénon potential and polynomial nonlinear source terms.Firstly,we establish the local well-posedness of model solution by using the theory of operator semigroups.Secondly,in view of the differential inequality,potential well theory and energy estimation,we analyze the conditions on finite time blow-up of the solution with non-positive initial energy.Moreover,we estimate the upper bound of blow-up time.Finally,at subcritical initial energy and critical initial energy,we give some conditions for the solutions existing globally or blowing up in finite time.In the third chapter,we study the initial-boundary value problem of a class of nonlinear viscoelastic equations with polynomial nonlinear source terms.Firstly,we establish the local well-posedness of the model solution by using the Faedo-Gal(?)rkin method.Secondly,in view of the differential inequalities,potential well theory and energy estimation,we analyze the conditions on global existence and uniformly bounded of the solution.Finally,we analyze the conditions on finite time blow-up of the solution with non-positive initial energy and positive initial energy.Moreover,we estimate the upper bound of blow-up time.