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

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

2007-05-23

arxiv.org/abs/0705.3362v1

Asymptotic Analysis, 54(1&2) (2007), 71?C92.

Mathematics

Analysis of PDEs

25 pages

Scientific paper

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.

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