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November  2006, 15(4): 1049-1078. doi: 10.3934/dcds.2006.15.1049

Complex transient patterns on the disk

Jonathan P. Desi 1, , Evelyn Sander 2, and  Thomas Wanner 2,

1. 

Department of Mathematics & Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, United States
2. 

Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, United States

Received  May 2005 Revised  November 2005 Published  May 2006

This paper studies spinodal decomposition in the Cahn-Hilliard model on the unit disk. It has previously been shown that starting at initial conditions near a homogeneous equilibrium on a rectangular domain, solutions to the linearized and the nonlinear Cahn-Hilliard equation behave indistinguishably up to large distances from the homogeneous state. In this paper we demonstrate how these results can be extended to nonrectangular domains. Particular emphasis is put on the case of the unit disk, for which interesting new phenomena can be observed. Our proof is based on vector-valued extensions of probabilistic methods used in Wanner [37]. These are the first results of this kind for domains more general than rectangular.
Keywords: Cahn-Hilliard equation., Phase separation, spinodal decomposition.
Mathematics Subject Classification: 35K55, 35B05, 35B25, 35P1.
Citation: Jonathan P. Desi, Evelyn Sander, Thomas Wanner. Complex transient patterns on the disk. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1049-1078. doi: 10.3934/dcds.2006.15.1049
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