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crystalline motion

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Motion of spirals by crystalline curvature
Hitoshi Imai, Naoyuki Ishimura, TaKeo Ushijima
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 4 / July 1999

Published online by Cambridge University Press:

15 August 2002, pp. 797-806

Print publication:

July 1999
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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.