Convergence to equilibrium for a Cahn-Hilliard model with the Wentzell boundary condition

摘要

In this paper we consider a Cahn-Hilliard model endowed with the Wentzell boundary condition, which arises from the study of spinodal decomposition in binary mixtures confined to a bounded domain with permeable wall. Under the assumption that the nonlinearity is analytic with respect to the unknown dependent function, we prove the convergence of a global solution to an equilibrium as time goes to infinity by means of an extended Lojasiewicz-Simon type inequality with boundary term. Estimates of the convergence rate are also obtained.