Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: An Allen-Cahn/Cahn-Hilliard System
Speaker: Amy Novick-Cohen, Technion---Israel Institute of Technology and Courant Institute, NYU
Date: Thursday, February 16, 2006 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
An Allen-Cahn/Cahn-Hilliard system was derived in 1994 to describe simulateous phase separation and ordering, in isothermal systems. When concentration dependence of the mobility is taken into account, a degenerate coupled fourth and second order parabolic system is obtained. At low temperatures and at near 50%-50% stiochiometry, formal asymptotics predict coupled surface diffusion and motion by mean curvature. This limiting system is important in and of itself in many contexts in materials science, and its relationship to various questions regarding wetting and spreading is also of interest. In terms of the regularity properites of the system, while existence, uniqueness, and long time behavior have been analyzed in depth in the constant mobility case, the regularity properties for the degenerate system are far more elusive. Indeed, so far for the degenerate system, existence has only been proven in one-dimension and the possibility of nonuniqueness has been demonstrated. It can also be shown to have many features in common with the thin film equations, and techniques developed in that context are relevant here.