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

摘要

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