Hyperbolic flow by mean curvature

A hyperbolic flow by mean curvature equation, v(t) + yv = k, for the evolut ion of interfaces is studied. Here v, k and v(t) are the normal velocity, c urvature and normal acceleration of the interface. A crystalline algorithm is developed for the motion of closed convex polygonal curves; such curves may exhibit damped oscillations and their shape appears to rotate during th e evolutionary process. The motion of circular interfaces is also studied b oth analytically and numerically. (C) 1999 Elsevier Science B.V. All rights reserved. PACS: 64.70.Dv.