Motion of spirals by crystalline curvature

Hitoshi Imai; Naoyuki Ishimura; TaKeo Ushijima

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 4, page 797-806
  • ISSN: 0764-583X

Abstract

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Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.

How to cite

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Imai, Hitoshi, Ishimura, Naoyuki, and Ushijima, TaKeo. "Motion of spirals by crystalline curvature." ESAIM: Mathematical Modelling and Numerical Analysis 33.4 (2010): 797-806. <http://eudml.org/doc/197602>.

@article{Imai2010,
abstract = { Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution. },
author = {Imai, Hitoshi, Ishimura, Naoyuki, Ushijima, TaKeo},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Crystalline motion; spiral-shaped polygonal curves; material sciences.; evolution equations; curvature; kinematic energies; local existence; uniqueness; solution},
language = {eng},
month = {3},
number = {4},
pages = {797-806},
publisher = {EDP Sciences},
title = {Motion of spirals by crystalline curvature},
url = {http://eudml.org/doc/197602},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Imai, Hitoshi
AU - Ishimura, Naoyuki
AU - Ushijima, TaKeo
TI - Motion of spirals by crystalline curvature
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 4
SP - 797
EP - 806
AB - Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
LA - eng
KW - Crystalline motion; spiral-shaped polygonal curves; material sciences.; evolution equations; curvature; kinematic energies; local existence; uniqueness; solution
UR - http://eudml.org/doc/197602
ER -

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