Motion of spirals by crystalline curvature
Hitoshi Imai, Naoyuki Ishimura, Takeo Ushijima · ESAIM Mathematical Modelling and Numerical Analysis · 1999
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.