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

Abstract

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 Łojasiewicz–Simon type inequality with boundary term. Estimates of the convergence rate are also obtained.