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Motion of a droplet by surface tension along the boundary
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Original article
Motion of a droplet by surface tension along the boundary
Nicholas D. Alikakos1, Xinfu Chen3 and Giorgio Fusco4
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Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA, US |
| (2) |
University of Athens, Panepistimiopolis, GR-15784, Athens, Greece, GR |
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Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA, US |
| (4) |
Dipartimento Di Mathematica, Universitá Di L' Aquila, L' Aquila, Italy, IT |
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.
Mathematics Subject Classification (1991): 35A35, 35C20, 35K55, 35B25.
Received June 13, 1998 / Accepted October 23 1998 / Published online September 14, 2000
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