Motion of a droplet by surface tension along the boundary

Abstract.

We give a description of the ultimate dynamics for the simplest evolution equation compatible with the Van der Waals Free Energy. We establish existence of stable sets of solutions corresponding to the physical motion of a small, almost semicircular interface (droplet) intersecting the boundary of the domain and moving towards a point where the curvature has a local maximum. Our results represent a particular extension of the Equilibrium theory of Modica and Sternberg to the next dynamic level in the Morse decomposition of the flow.