Asymptotic behavior of a phase-field system with dynamic boundary conditions

This article is devoted to the study of the asymptotic behavior of aCaginalp phase-field system with nonlinear dynamic boundary conditions. As a proper parameter ε goes to zero, this problem converges to the viscous Cahn-Hilliard equation. We firstprove the existence and uniqueness of the solution to the system and then provide an upper semicontinuous family of globalattractors A_ε . Furthermore, we prove the existence of anexponential attractor for each problem, which yields, since it contains the aforementioned global attractor, the finite fractal dimensionality of A_ε.