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Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions. (English) Zbl 1304.35085
Summary: 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 Łojasiewicz-Simon inequality.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
80A22 Stefan problems, phase changes, etc.
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