WIAS Preprint No. 980, (2004)

A descent method for the free energy of multicomponent systems


  • Gajewski, Herbert
  • Griepentrog, Jens André

2010 Mathematics Subject Classification

  • 90C26 82B26 94A08


  • Nonconvex functionals, Cahn-Hilliard equation, Lyapunov function, asymptotic behaviour, phase separation, image segmentation




Equilibrium distributions of a multicomponent system minimize the free energy functional under the constraint of mass conservation of the components. However, since the free energy is not convex in general, one tries usually 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.

Appeared in

  • Discrete Contin. Dyn. Syst., 15 (2006) pp. 505--528.

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