Well-posedness And Exponential Attractor Of The Conserved Phase-field Model

In this thesis,we study a class of conserved phase-field models for mass conservation,which are obtained by coupling the Cahn-Hilliard equation with the heat equation.Based on the restrictions of the nonlinear term in general form,we discuss the well-posedness and existence of exponential attractors of the model,solve the problems of uniqueness and existence of the solution of equations and existence of exponential attractors.The main tasks are as follows.The priori estimation of the solution of the equation is given with common inequalities and existing conclusions,and the norm is bounded so as to prove the existence of the solution.The uniqueness of the solution is obtained by making a difference and combining with Gronwall lemma.Finally,the existence of the exponential attractor is proved by the existence lemma of exponential attractor.In the thesis,the assumption of nonlinear term is no longer a special function,but a set of more general restrictions,which breaks the restriction of the original problem that nonlinear term is a special function type and expands the application scope of the model.