Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions
Articolo
Data di Pubblicazione:
2014
Citazione:
Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions / C. Cavaterra, M. Grasselli, H. Wu. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 13:5(2014), pp. 1855-1890.
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Cattaneo's law; Convergence to equilibrium; Existence and uniqueness; Global attractors; Inertial term; Viscous Cahn-Hilliard equation
Elenco autori:
C. Cavaterra, M. Grasselli, H. Wu
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