# American Institute of Mathematical Sciences

November  2011, 30(4): 1037-1054. doi: 10.3934/dcds.2011.30.1037

## Asymptotics for a generalized Cahn-Hilliard equation with forcing terms

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

Received  February 2010 Revised  July 2010 Published  May 2011

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.
Citation: Dimitra Antonopoulou, Georgia Karali, Georgios T. Kossioris. Asymptotics for a generalized Cahn-Hilliard equation with forcing terms. Discrete & Continuous Dynamical Systems - A, 2011, 30 (4) : 1037-1054. doi: 10.3934/dcds.2011.30.1037
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