Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions
Cecilia Cavaterra, Maurizio Grasselli, Hao Wu · Communications on Pure & Applied Analysis · 2014
We consider a non-isothermal modified viscous Cahn-Hilliard equation which was previously analyzed by M. Grasselli et al.Such an equation is characterized by an inertial term and it is coupled with a hyperbolic heat equation from the Maxwell-Cattaneo's law.We analyze the case in which the order parameter is subject to a dynamic boundary condition.This assumption requires a more refined strategy to extend the previous results to the present case.More precisely, we first prove the well-posedness for solutions with finite energy as well as for weak solutions.Then we establish the existence of a global attractor. Finally, we prove the convergence of any given weak solution to a single equilibriumby using a suitable Łojasiewicz-Simon inequality.