The Research On The Existence Of Attractors For Some Kinds Of Partial Differential Equations

In this dissertation,we mainly consider Plate equation and beam equation from the perspective of dynamical system,and use discrete squeeze,prior estimation,operator decomposition and compression function methods to prove the existence of attractors under different conditions.First,we discuss the existence of the exponential attractor for the Plate equation on a bounded region?Ωwith smooth boundaries.Based on previous studies,Lipschitz continuous and discrete squeeze conditions are used in phase spaceE₀ to prove the existence of exponent attractors for the Plate equation.Secondly,we study the existence of the time-dependent global attractors for the beam equation.When the non-linear term f satisfies the critical growth conditions,based on the existence theorem of the time-dependent global attractor,the coefficient parameters is time-dependent are verified by applying prior estimation and operator decomposition methods.As time-dependent,the asymptotic compactness of the family{U（t,?）}of processes corresponding to the beam equation results in the existence and regularity of the time-dependent global attractors for the beam equation.Finally,we study the existence of the time-dependent pullback attractors for the beam equation.When the non-linear term f satisfies the critical growth conditions,it is?（t）a positive monotonically decreasing function and tends to 0,and the external force term is not time-dependent.The compression function is used to verify the asymptotic tightness of the pullback family of equation solution sets,and the existence of time-dependent pullback attractors for non-autonomous beam equations with time-depen-ent coefficients is proved.