On the 2D Cahn-Hilliard Equation with Inertial Term

Grasselli, M, Schimperna, G and Zelik, S (2009) On the 2D Cahn-Hilliard Equation with Inertial Term Communications in Partial Differential Equations, 34 (2), PII 909499. pp. 137-170.

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Abstract

Galenko et al. proposed a modified Cahn-Hilliard equation to model rapid spinodal decomposition in non-equilibrium phase separation processes. This equation contains an inertial term which causes the loss of any regularizing effect on the solutions. Here we consider an initial and boundary value problem for this equation in a two-dimensional bounded domain. We prove a number of results related to well-posedness and large time behavior of solutions. In particular, we analyze the existence of bounded absorbing sets in two different phase spaces and, correspondingly, we establish the existence of the global attractor. We also demonstrate the existence of an exponential attractor.

Item Type:	Article
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Grasselli, M, Schimperna, G and Zelik, S
Date :	1 January 2009
DOI :	10.1080/03605300802608247
Copyright Disclaimer :	This is the arXiv version of an article published by Taylor & Francis in Communications in Partial Differential Equations on 12 March 2009 available online: http://www.tandfonline.com/10.1080/03605300802608247
Uncontrolled Keywords :	Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, MATHEMATICS, MATHEMATICS, APPLIED, Absorbing sets, Cahn-Hilliard equation, Exponential attractors, Global attractors, Logarithmic embedding inequality, Nonconvex potential, DYNAMIC BOUNDARY-CONDITIONS, UNIFORM EXPONENTIAL ATTRACTORS, DAMPED WAVE-EQUATION, LONG-TIME BEHAVIOR, PHASE-FIELD SYSTEM, SPINODAL DECOMPOSITION, GLOBAL ATTRACTORS, HYPERBOLIC RELAXATION, SINGULAR PERTURBATIONS, ASYMPTOTIC-BEHAVIOR
Related URLs :	Author
Additional Information :	This is the arXiv version of an article published by Taylor & Francis in Communications in Partial Differential Equations on 12 March 2009 available online: http://www.tandfonline.com/10.1080/03605300802608247
Depositing User :	Symplectic Elements
Date Deposited :	02 Mar 2016 14:24
Last Modified :	06 Jul 2019 05:15
URI:	http://epubs.surrey.ac.uk/id/eprint/809937

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