Anisotropic motion of a phase interface.

1. The model. In the model we assumed that at time t the solid occupies a region Ω (t) c i? whose boundary dQ(t) is a piecewise smooth (C, say) curve, with a finite number of corners Ρ^(ί)9..., /#(0· We derived two equations for the time evolution of Ω (t) (i.e. of its boundary). The first of these two equations is a relation between the normal velocity of any point Q on the boundary, and the orientation and curvature of the front dQ(t) at this particular point Q, and time /. The other equation arises from the requirement that the capillary force be continuous at the corner points Pt(t),...,PN(t).