Research On Attractors Problem Of Cahn-hilliard Equations With Inertial Term

As an important reaction-diffusion equation,Cahn-Hilliard equation can well explain the diffusion phenomena widely existing in nature.In this paper,we study the existence of attractors for Cahn-Hilliard equations with inertial term.When the nonlinear term f meet different conditions,the existence of attractors of the equation is proved by using appropriate methods.The details are as follows:Firstiy,the pullback attractor of Cahn-Hilliard equation with inertial term is studied.In the case that the nonlinear term satisfies the regularity condition and the external term is time-independent,the existence of the weak solutions of the equation inH~2（Ω）∩H₀~1（Ω）is obtained by using the Faedo-Galerkin method,the asymptotic compactness of the pullback absorbing set is obtained by using the contraction function method,and then the existence of the pullback attractor of the equation is obtained.Secondly,after proving the fitness of weak solutions of Cahn-Hilliard equation with inertial term,the continuity and asymptotic compactness of the process family U generated in H and V are obtained,the existence of the uniform attractor of the equation is obtained by means of the uniform condition（C）.Finally,the exponential attractor of viscous Cahn-Hilliard equation with inertial term is studied.Based on the existence theorem of exponential attractor,the Lipschitz continuity of semigroups in space H is proved.And using the operator decomposition to obtain the existence of exponential attractor.