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 equilibrium by using a suitable Lojasiewicz-Simon inequality.
|Titolo:||Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions|
CAVATERRA, CECILIA (Primo)
|Parole Chiave:||Cattaneo's law; Convergence to equilibrium; Existence and uniqueness; Global attractors; Inertial term; Viscous Cahn-Hilliard equation|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2014|
|Digital Object Identifier (DOI):||10.3934/cpaa.2014.13.1855|
|Appare nelle tipologie:||01 - Articolo su periodico|