Diffuse-interface treatment of the anisotropic mean-curvature flow

Applications of Mathematics

Volumn 48, Issue 6, 2003, Pages 437-453

  Beneš, Michal ^a  

^a CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

FDM; Finsler geometry; mean curvature flow; phase field method

Indexed keywords

EID: 84867968035     PISSN: 08627940     EISSN: 15729109     Source Type: Journal    
DOI: 10.1023/B:APOM.0000024485.24886.b9     Document Type: Article

References (19)

1. G. Bellettini M. Novaga M. Paolini 2001 Characterization of facet-breaking for nonsmooth mean curvature ow in the convex case Interfaces and Free Boundaries 3 415 446 (Pubitemid 33360839)
2. G. Bellettini M. Paolini 1996 Anisotropic motion by mean curvature in the context of Finsler geometry Hokkaido Math. J. 25 537 566
3. M. Beneš: Anisotropic phase-field model with focused latent-heat release. In: Free Boundary Problems: Theory and Applications II, GAKUTO International Series Mathematical Sciences and Applications, Vol. 14. Chiba, Japan, 2000, pp. 18-30.
4. M. Beneš 2001 Mathematical analysis of phase-field equations with numerically efficient coupling terms Interfaces and Free Boundaries 3 201 221
5. M. Beneš 2001 Mathematical and computational aspects of solidification of pure substances Acta Math. Univ. Comenian. 70 123 152
6. M. Beneš K. Mikula 1998 Simulation of anisotropic motion by mean curvature-comparison of phase-field and sharp-interface approaches Acta Math. Univ. Comenian. 67 17 42
7. L. Bronsard R. Kohn 1991 Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics J. Differential Equations 90 211 237
8. G. Caginalp 1986 An analysis of a phase field model of a free boundary Arch. Rational Mech. Anal. 92 205 245
9. C. M. Elliott M. Paolini R. Schatzle 1996 Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean curvature flow Math. Models Methods Appl. Sci. 6 1103 1118
10. L. C. Evans J. Spruck 1991 Motion of level sets by mean curvature I. J. Differential Geom. 33 635 681
11. Y. Giga M. Paolini P. Rybka 2001 On the motion by singular interfacial energy Japan J. Indust. Appl. Math. 18 47 64
12. M. Gurtin 1986 On the two-phase Stefan problem with interfacial energy and entropy Arch. Rational Mech. Anal. 96 200 240
13. M. Gurtin: Thermomechanics of Evolving Phase Boundaries in the Plane. Clarendon Press, Oxford, 1993.
14. D. A. Kessler J. Koplik H. Levine 1985 Geometrical models of interface evolution. III. Theory of dendritic growth Phys. Rev. A 31 1712 1717
15. J.-L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod Gauthier-Villars, Paris, 1969.
16. T. Ohta M. Mimura R. Kobayashi 1989 Higher-dimensional localized patterns in excitable media Physica D 34 115 144
17. J. A. Sethian: Level Set Methods. Cambridge University Press, New York, 1996.
18. R. Temam: Navier-Stokes Equations, Theory and Numerical Analysis. North-Holland, Amsterdam, 1979.
19. A. Visintin: Models of Phase Transitions. Birkhäuser, Boston, 1996.