The Research Of Time-Dependent Attractors For Some Kinds Of Partial Differential Equations

Partial differential equations in infinite-dimensional dynamical systems are often used to study changes in biological sciences,chaotic phenomena,chemical engineering,physics and other fields,and time-dependent attractors play a very important role as one of the tools to describe the asymptotic behavior of solutions of infinitedimensional dynamical systems.In this paper,the time-dependent attractors existence of the beam equations,the Berger equations and the nonclassical reaction diffusion equations are studied.Firstly,the beam equations have many applications in the construction of tunnel and bridges.The time-dependent existence of global attractors for beam equations with linear memory on the bounded region with smooth boundaries ?Ω are discussed.The prior estimation and operator decomposition methods are used to verify the asymptotic compactness of the process family corresponding to the equations when the coefficient parameters are time-dependent,so as to obtain the existence and regularity of the equations time-dependent global attractors.Secondly,the time-dependent existence of global attractors of the Berger equations with linear memory when there is no external force in the sense of weak damping are studied.The existence of the bounded absorption set of the process family is obtained by applying the method of prior estimation,and the asymptotic compactness of the process is verified by applying the shrinkage function method to obtain the existence of the equations time-dependent global attractors.Finally,the time-dependent existence of global attractors in non-classical reactiondiffusion equations with derivative terms are studied.Based on the time-dependent global attractors existence theorem,the method of prior estimation and contraction function is applied to verify the bounded suction collection and compactness of the process,thus confirming the existence of the equations time-dependent attractors.In the dissertation enriches the time-dependent attractors of infinite-dimensional dynamical systems through the study of several types of time-dependent partial differential equations,providing effective methods for analyzing the long-term behavior of solutions to such problems in the future.