论文信息 - A descent method for the free energy of multicomponent systems

A descent method for the free energy of multicomponent systems

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.

Herbert Gajewski | Jens Andre Griepentrog

[1] Jean-Michel Morel,et al. Variational methods in image segmentation , 1995 .

[2] Macroscopic evolution of particle systems with short- and long-range interactions , 2000, cond-mat/0003259.

[3] A non-smooth version of the Lojasiewicz–Simon theorem with applications to non-local phase-field systems , 2004 .

[4] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[5] Herbert Gajewski,et al. On a nonlocal phase separation model , 2003 .

[6] P. C. Fife,et al. NONLOCAL MODELS OF PHASETRANSITIONS IN , .

[7] Theorie der Lösungsverzweigung bei nichtlinearen Gleichungen , 1973 .

[8] Klaus Gärtner,et al. On a nonlocal model of image segmentation , 2005 .

[9] J. Dieudonné. Grundzüge der modernen Analysis , 1976 .

[10] Peter W. Bates,et al. An Integrodifferential Model for Phase Transitions: Stationary Solutions in Higher Space Dimensions , 1999 .

[11] J. Griepentrog. Linear Elliptic Boundary Value Problems with Non-smooth Data: Campanato Spaces of Functionals , 2002 .

[12] Ralph Chill,et al. On the Łojasiewicz–Simon gradient inequality , 2003 .

[13] Local and asymptotic analysis of the flow generated by the Cahn–Hilliard–Gurtin equations , 2006 .

[14] J. Griepentrog. On the unique solvability of a nonlocal phase separation problem for multicomponent systems , 2004 .