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

Article type: Research Article

Authors: Wu, Hao

Affiliations: School of Mathematical Sciences, Fudan University, 200433 Shanghai, PR China. E-mail: [email protected]

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.

Keywords: Cahn–Hilliard equation, Wentzell boundary condition, Łojasiewicz–Simon inequality, convergence to equilibrium

Journal: Asymptotic Analysis, vol. 54, no. 1-2, pp. 71-92, 2007