Well-posedness And Maximum Modulus Estimate For The Solution Of The Nonlocal Convective Cahn-Hilliard Equation

In this thesis,the well-posedness and maximum modulus estimate for the solution of the nonlocal convective Cahn-Hilliard equation with Neumann boundary condition are studied.The convective Cahn-Hilliard equation can describe many physical phenomena,such as binary alloys in phase separation systems and the growth of thermodynamically unstable crystal surfaces.The maximum modulus estimate of the solution is obtained by an iterative method,which is based on the Nirenberg-Gagliardo inequality and developed by Bates P.W.in[BATES P W.On some nonlocal evolution equations arising in materials science[M]//Fields Institute Communications.Nonlinear dynamics and evolution equations.Providence:American Mathematical Society,2006:13-52.].And the existence of the classical solution for this equation is proved by employing the the Leray-Schauder fixed point theorem.Also,the existence and uniqueness of the weak solution are studied by the weak convergence method.Finally,the long time behavior of the solution in the Lp(Ω)is discussed.