Asymptotics for a generalized Cahn-Hilliard equationwith forcing terms

Dimitra Antonopoulou; Georgia Karali; Georgios T. Kossioris

doi:10.3934/dcds.2011.30.1037

Article Contents

2011, Volume 30, Issue 4: 1037-1054. Doi: 10.3934/dcds.2011.30.1037

This issue Previous Article Dispersive estimates using scattering theory for matrix Hamiltonian equations Next Article On the location of a peak point of a least energy solution for Hénon equation

Asymptotics for a generalized Cahn-Hilliard equation with forcing terms

1.
Department of Applied Mathematics, University of Crete, 714 09 Heraklion
2.
Department of Mathematics, University of Crete, GR-714 09 Heraklion, Crete

Received: January 31, 2010

Revised: June 30, 2010

Published: September 2011

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Abstract

Motivated by the physical theory of Critical Dynamics the Cahn-Hilliard equation on a bounded space domain is considered and forcing terms of general type are introduced. For such a rescaled equation the limiting inter-face problem is studied and the following are derived: (i) asymptotic results indicating that the forcing terms may slow down the equilibrium locally or globally, (ii) the sharp interface limit problem in the multidimensional case demonstrating a local influence in phase transitions of terms that stem from the chemical potential, while free energy independent terms act on the rest of the domain, (iii) a limiting non-homogeneous linear diffusion equation for the one-dimensional problem in the case of deterministic forcing term that follows the white noise scaling.

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Mathematics Subject Classification: Primary: 35K55, 35K57.

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