TITLE

NON-ISOTHERMAL VISCOUS CAHN-HILLIARD EQUATION WITH INERTIAL TERM AND DYNAMIC BOUNDARY CONDITIONS

AUTHOR(S)
CAVATERRA, CECILIA; GRASSELLI, MAURIZIO; WU, HAO
PUB. DATE
September 2014
SOURCE
Communications on Pure & Applied Analysis;Sep2014, Vol. 13 Issue 5, p1855
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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
ACCESSION #
97909576

 

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