A descent method for the free energy of multicomponent systems

Abstract

Equilibrium distributions of multicomponent systems minimize the free energyfunctional 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 distributionsas 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 isestablished and applied to phase separation problems in multicomponentsystems and image segmentation.