Research On Pullback Exponential Attractor For Several Types Of Nonlinear Development Equations

The pullback exponential attractor,belonging to a positive invariant minimum compact set family with finite fractal dimension and attracting any bounded subset in phase space at an exponential rate,is a useful tool to study the asymptotic behavior of infinite-dimensional dynamical systems.This dissertation has explored the existence of two-dimensional g-Navier-Stokes equations,strong damping wave equations,and non-classical reaction diffusion equations pullback exponential attractor.First,the existence of the pullback exponential attractor for the two-dimensional gNavier-Stokes equations with nonlinear damping are considered.The existence and uniqueness of the global weak solution are proved by Galerkin method,and the uniformly asymptotic compactness of the solution process is proved by energy method,and then the existence of the pullback exponential attractor is proved.Second,based on the existence theorem of orbital attractor and global attractor,the existence of the pullback exponential attractor of the memorized strong damping wave equations are proved by the new abstract result analysis of the construction of the pullback exponential attractor in literature,and the decomposition method is used.Finally,considering the viscoelasticity of the propagation medium,the decay memory is added to the non-classical reaction diffusion equations,the existence of the bounded absorption set is verified by prior estimation,and the operator decomposition method is used to divide the equation into two parts.One part satisfies regularity and the other part satisfies contraction,and the existence of pullback exponential attractor with non-classical reaction diffusion equations with memory is obtained.The study of the pullback exponential attractor of nonlinear evolution equations provides a new idea for the follow-up research and enriches the theoretical research in this field.