Well-posedness and long-time behavior for a nonstandard viscous   Cahn-Hilliard system
  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. 
Pierluigi Colli, Gianni Gilardi, Paolo Podio-Guidugli, Juergen   Sprekels
math.AP