A Hyperbolic Theory for the Evolution of Plane Curves
Morton E. Gurtin, Paolo Podio–Guidugli · SIAM Journal on Mathematical Analysis · 1991
A theory is developed for the evolution of plane curves. This theory is based on balance laws for mass and momentum in conjunction with constitutive equations appropriate to a phase interface such as that between a crystal and its melt. The resulting evolution equation is hyperbolic and has solutions with aspects qualitatively reminiscent of the melting-freezing waves observed at the surface of ${\text{He}}^4 $ crystals.