Motion of a droplet by surface tension along the boundary

We give a description of the ultimate dynamics for the simplest evolution e quation compatible with the Van der Waals Free Energy. We establish existen ce of stable sets of solutions corresponding to the physical motion of a sm all, almost semicircular interface (droplet) intersecting the boundary of t he domain and moving towards a point where the curvature has a local maximu m, Our results represent a particular extension of the Equilibrium theory o f Modica and Sternberg to the next dynamic level in the Morse decomposition of the flow.