Computational studies of non-local anisotropic Allen-Cahn equation
Michal Beneš; Shigetoshi Yazaki; Masato Kimura
Mathematica Bohemica (2011)
- Volume: 136, Issue: 4, page 429-437
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topBeneš, Michal, Yazaki, Shigetoshi, and Kimura, Masato. "Computational studies of non-local anisotropic Allen-Cahn equation." Mathematica Bohemica 136.4 (2011): 429-437. <http://eudml.org/doc/197198>.
@article{Beneš2011,
abstract = {The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.},
author = {Beneš, Michal, Yazaki, Shigetoshi, Kimura, Masato},
journal = {Mathematica Bohemica},
keywords = {Allen-Cahn equation; phase transitions; mean-curvature flow; finite-difference method; Allen-Cahn equation; phase transitions; mean-curvature flow; finite-difference method},
language = {eng},
number = {4},
pages = {429-437},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Computational studies of non-local anisotropic Allen-Cahn equation},
url = {http://eudml.org/doc/197198},
volume = {136},
year = {2011},
}
TY - JOUR
AU - Beneš, Michal
AU - Yazaki, Shigetoshi
AU - Kimura, Masato
TI - Computational studies of non-local anisotropic Allen-Cahn equation
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 4
SP - 429
EP - 437
AB - The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.
LA - eng
KW - Allen-Cahn equation; phase transitions; mean-curvature flow; finite-difference method; Allen-Cahn equation; phase transitions; mean-curvature flow; finite-difference method
UR - http://eudml.org/doc/197198
ER -
References
top- Rubinstein, J., Sternberg, P., 10.1093/imamat/48.3.249, IMA J. Appl. Math. (1992), 48 249-264. (1992) MR1167735DOI10.1093/imamat/48.3.249
- Allen, S., Cahn, J., A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metall. (1979), 27 1084-1095. (1979)
- Cahn, J. W., Hilliard, J. E., 10.1063/1.1730447, J. Chem. Phys. (1959), 31 688-699. (1959) DOI10.1063/1.1730447
- Taylor, J. E., Cahn, J. W., 10.1007/BF02186838, J. Statist. Phys. (1994), 77 183-197. (1994) Zbl0844.35044MR1300532DOI10.1007/BF02186838
- Bronsard, L., Kohn, R., 10.1016/0022-0396(91)90147-2, J. Differential Equations (1991), 90 211-237. (1991) Zbl0735.35072MR1101239DOI10.1016/0022-0396(91)90147-2
- Bronsard, L., Stoth, B., 10.1137/S0036141094279279, SIAM J. Math. Anal. (1997), 28 769-807. (1997) Zbl0874.35009MR1453306DOI10.1137/S0036141094279279
- Beneš, M., 10.1023/B:APOM.0000024485.24886.b9, Appl. Math., Praha (2003), 48 437-453. (2003) Zbl1099.53044MR2025297DOI10.1023/B:APOM.0000024485.24886.b9
- Beneš, M., Mathematical and computational aspects of solidification of pure substances, Acta Math. Univ. Comenian. (2001), 70 123-152. (2001) Zbl0990.80006MR1865364
Citations in EuDML Documents
topNotesEmbed ?
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.