Convergence to Equilibrium for the Cahn-Hilliard Equation with Wentzell Boundary Condition

In this paper we consider the Cahn-Hilliard equation endowed with Wentzell boundary condition which is a model of phase separation in a binary mixture contained in a bounded domain with permeable wall. Under the assumption that the nonlinearity is analytic with respect to unknown dependent function, we prove the convergence of a global solution to an equilibrium as time goes to infinity by means of a suitable \L ojasiewicz-Simon type inequality with boundary term. Estimates of convergence rate are also provided.