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May  2006, 15(2): 505-528. doi: 10.3934/dcds.2006.15.505

A descent method for the free energy of multicomponent systems

Herbert Gajewski 1, and  Jens A. Griepentrog 1,

1. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany, Germany

Received  March 2005 Revised  December 2005 Published  March 2006

Equilibrium distributions of multicomponent systems minimize the free energy functional under the constraint of mass conservation of the components. However, since the free energy is not convex in general, usually one tries to characterize and to construct equilibrium distributions as steady states of an adequate evolution equation, for example, the nonlocal Cahn-Hilliard equation for binary alloys. In this work a direct descent method for nonconvex functionals is established and applied to phase separation problems in multicomponent systems and image segmentation.
Keywords: asymptotic behaviour, Lyapunov function, phase separation, image segmentation., Nonconvex functionals, Cahn-Hilliard equation.
Mathematics Subject Classification: 90C26, 82B26, 94A0.
Citation: Herbert Gajewski, Jens A. Griepentrog. A descent method for the free energy of multicomponent systems. Discrete & Continuous Dynamical Systems, 2006, 15 (2) : 505-528. doi: 10.3934/dcds.2006.15.505
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