Existence Of Exponential Attractors For Boussinesq Equations With Memory-Type

In this dissertation,we prove the existence of the exponential attractor of the memory-type Boussinesq equation by using the infinite dimensional dynamical sys-tem theory and the operator semi-group decomposition technique.The main con-tents are:In the first part,the development background and research status of Boussinesq equation are introduced.In the second part,some basic concepts and abstract results of the existence of exponential attractors are given.In the third part,the existence of the exponential attractor of Boussinesq equa-tion with strong damping is studied.Firstly,we take advantage of energy estimation method to prove the existence of bounded absorbing set in H-1(?)× H01(?)and L2(?)× H2(?)? H01(?);Secondly,the existence of the exponential attractor is obtained by using the operator decomposition method,and then finite fractal di-mension of the global attractor is also acquired.In the fourth part,the existence of exponential attractor for Boussinesq equa-tion with memory is studied.This part is based on the previous part and we taking the memory term into account in the equation.First of all,we prove the exis-tence of bounded absorbing set and compactness of the corresponding semigroup by constructing relatively complex ternary solution space and some more complex and detailed estimates are made on the space;Secondly,the equation of the existence of exponential attractor is gained by using operator decomposition technique.