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On a new kind of convexity for solutions of parabolic problems
On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect
1. | Shibaura Institute of Technology, Fukasaku 309, Minuma-ku, Saitama, 337-8570, Japan |
References:
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doi: doi:10.1007/BF01041068. |
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Y. Giga and M. E. Gurtin, A comparison theorem for crystalline evolution in the plane, Quart. J. Appl. Math., LIV (1996), 727-737. |
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M. E. Gurtin, "Thermomechanics of Evolving Phase Boundaries in the Plane," Oxford, Clarendon Press, 1993. |
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T. Ishiwata, Motion of non-convex polygons by crystalline curvature and almost convexity phenomena, Japan Journal of Industrial and Applied Mathematics, 25 (2008), 233-253.
doi: doi:10.1007/BF03167521. |
[5] |
Y. Marutani, H. Ninomiya and R. Weidenfeld, Traveling curved fronts of anisotropic curvature flows, Japan Journal of Industrial and Applied Mathematics, 23 (2006), 83-104.
doi: doi:10.1007/BF03167500. |
[6] |
S. Yazaki, Point-extinction and geometric expansion of solutions to a crystalline motion, Hokkaido Math. J., 30 (2001), 327-357. |
show all references
References:
[1] |
S. Angenent and M. E. Gurtin, Multiphase thermomechanics with interfacial structure, 2. Evolution of an isothermal interface, Arch. Rational Mech. Anal., 108 (1989), 323-391.
doi: doi:10.1007/BF01041068. |
[2] |
Y. Giga and M. E. Gurtin, A comparison theorem for crystalline evolution in the plane, Quart. J. Appl. Math., LIV (1996), 727-737. |
[3] |
M. E. Gurtin, "Thermomechanics of Evolving Phase Boundaries in the Plane," Oxford, Clarendon Press, 1993. |
[4] |
T. Ishiwata, Motion of non-convex polygons by crystalline curvature and almost convexity phenomena, Japan Journal of Industrial and Applied Mathematics, 25 (2008), 233-253.
doi: doi:10.1007/BF03167521. |
[5] |
Y. Marutani, H. Ninomiya and R. Weidenfeld, Traveling curved fronts of anisotropic curvature flows, Japan Journal of Industrial and Applied Mathematics, 23 (2006), 83-104.
doi: doi:10.1007/BF03167500. |
[6] |
S. Yazaki, Point-extinction and geometric expansion of solutions to a crystalline motion, Hokkaido Math. J., 30 (2001), 327-357. |
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