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On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potential
2014, Colli, Pierluigi, Gilardi, Gianni, Sprekels, Jürgen
The Cahn-Hilliard and viscous Cahn-Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved.
Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system
2011, Colli, Pierluigi, Gilardi, Geanni, Podio-Guidugli, Paolo, Sprekels, Jürgen
We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a careful development of uniform estimates and the deduction of certain useful boundedness properties, we prove existence and uniqueness of a global-in-time smooth solution to the associated initial/boundary-value problem; moreover, we give a description of the relative $omega$-limit set.