Asymptotic Behavior Of Solutions Of Kirchhoff-Type Beam Equation With Linear Memory

In this paper,the Kirchhoff-Type beam equation with linear memory is studied by using infinite dimensional dynamical system and operator semigroup theory,the thesis is divided into four chapters:In the first chapter,this paper introduces the research background of beam equation,and expounds the main research ideas of this thesis.In the second chapter,we give the concepts of global attractor and exponential attractor.In the third chapter,we study the long-time behavior of the solution of KirchhoffType beam equation with linear memory and nonlinear damping.By using the method of energy estimation and constructing auxiliary function,the global attractors in weak topological space is obtained,partially generalizes the existing results.In the fourth part,the long-time behavior of the solution of Kirchhoff-Type beam equation with linear memory and linear damping is studied.First,energy estimation is used to obtain the bounded absorption set in the strong and weak space.Second,using the operator decomposition method,the exponential attractor in weak topological space is obtained.