A descent method for the free energy of multicomponent systems

Herbert Gajewski; Jens A. Griepentrog

doi:10.3934/dcds.2006.15.505

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2006, Volume 15, Issue 2: 505-528. Doi: 10.3934/dcds.2006.15.505

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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

Received: February 28, 2005

Revised: November 30, 2005

Published: March 2006

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Abstract

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.

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Mathematics Subject Classification: 90C26, 82B26, 94A08.

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