Diffuse-interface treatment of the anisotropic mean-curvature flow
Applications of Mathematics (2003)
- Volume: 48, Issue: 6, page 437-453
- ISSN: 0862-7940
Access Full Article
top
Abstract
topHow to cite
topBeneš, Michal. "Diffuse-interface treatment of the anisotropic mean-curvature flow." Applications of Mathematics 48.6 (2003): 437-453. <http://eudml.org/doc/33159>.
@article{Beneš2003,
abstract = {We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.},
author = {Beneš, Michal},
journal = {Applications of Mathematics},
keywords = {mean-curvature flow; phase-field method; FDM; Finsler geometry; mean-curvature flow; phase-field method; FDM; Finsler geometry},
language = {eng},
number = {6},
pages = {437-453},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Diffuse-interface treatment of the anisotropic mean-curvature flow},
url = {http://eudml.org/doc/33159},
volume = {48},
year = {2003},
}
TY - JOUR
AU - Beneš, Michal
TI - Diffuse-interface treatment of the anisotropic mean-curvature flow
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 6
SP - 437
EP - 453
AB - We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.
LA - eng
KW - mean-curvature flow; phase-field method; FDM; Finsler geometry; mean-curvature flow; phase-field method; FDM; Finsler geometry
UR - http://eudml.org/doc/33159
ER -
References
top- Characterization of facet-breaking for nonsmooth mean curvature flow in the convex case, Interfaces and Free Boundaries 3 (2001), 415–446. (2001) MR1869587
- 10.14492/hokmj/1351516749, Hokkaido Math. J. 25 (1996), 537–566. (1996) MR1416006DOI10.14492/hokmj/1351516749
- 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. (2000) MR1793055
- Mathematical analysis of phase-field equations with numerically efficient coupling terms, Interfaces and Free Boundaries 3 (2001), 201–221. (2001) Zbl0986.35116MR1825658
- Mathematical and computational aspects of solidification of pure substances, Acta Math. Univ. Comenian. 70 (2001), 123–152. (2001) Zbl0990.80006MR1865364
- Simulation of anisotropic motion by mean curvature-comparison of phase-field and sharp-interface approaches, Acta Math. Univ. Comenian. 67 (1998), 17–42. (1998) MR1660813
- 10.1016/0022-0396(91)90147-2, J. Differential Equations 90 (1991), 211–237. (1991) MR1101239DOI10.1016/0022-0396(91)90147-2
- 10.1007/BF00254827, Arch. Rational Mech. Anal. 92 (1986), 205–245. (1986) Zbl0608.35080MR0816623DOI10.1007/BF00254827
- Interface estimates for the fully anisotropic Allen-Cahn equation and anisotropic mean curvature flow, Math. Models Methods Appl. Sci. 6 (1996), 1103–1118. (1996) MR1428147
- 10.4310/jdg/1214446559, J. Differential Geom. 33 (1991), 635–681. (1991) MR1100206DOI10.4310/jdg/1214446559
- On the motion by singular interfacial energy, Japan J. Indust. Appl. Math. 18 (2001), 47–64. (2001) MR1842909
- On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96 (1986), 200–240. (1986) Zbl0654.73008MR0855304
- Thermomechanics of Evolving Phase Boundaries in the Plane, Clarendon Press, Oxford, 1993. (1993) Zbl0787.73004MR1402243
- Geometrical models of interface evolution. III. Theory of dendritic growth, Phys. Rev. A 31 (1985), 1712–1717. (1985)
- Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod Gauthier-Villars, Paris, 1969. (1969) Zbl0189.40603MR0259693
- 10.1016/0167-2789(89)90230-3, Physica D 34 (1989), 115–144. (1989) MR0982383DOI10.1016/0167-2789(89)90230-3
- Level Set Methods, Cambridge University Press, New York, 1996. (1996) Zbl0868.65059MR1409367
- Navier-Stokes Equations, Theory and Numerical Analysis, North-Holland, Amsterdam, 1979. (1979) Zbl0426.35003MR0603444
- Models of Phase Transitions, Birkhäuser, Boston, 1996. (1996) Zbl0882.35004MR1423808
Citations in EuDML Documents
top- Pavel Strachota, Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation
- Michal Beneš, Shigetoshi Yazaki, Masato Kimura, Computational studies of non-local anisotropic Allen-Cahn equation
- Tomáš Oberhuber, Atsushi Suzuki, Vítězslav Žabka, The CUDA implementation of the method of lines for the curvature dependent flows
- Miroslav Kolář, Michal Beneš, Daniel Ševčovič, Computational studies of conserved mean-curvature flow
- Dieu Hung Hoang, Michal Beneš, Forced anisotropic mean curvature flow of graphs in relative geometry
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.