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Original article

Motion of a droplet by surface tension along the boundary

Nicholas D. Alikakos1, Xinfu Chen3 and Giorgio Fusco4

(1)  Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA, US
(2)  University of Athens, Panepistimiopolis, GR-15784, Athens, Greece, GR
(3)  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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Referenced by
4 newer articles

  1. Malchiodi, Andrea (2007) Boundary-clustered interfaces for the Allen–Cahn equation. Pacific Journal of Mathematics 229(2)
    [CrossRef]
  2. Pino, Manuel (2008) The Toda System and Clustering Interfaces in the Allen–Cahn equation. Archive for Rational Mechanics and Analysis
    [CrossRef]
  3. Chen, Xinfu (2005) Periodicity and Uniqueness of Global Minimizers of an Energy Functional Containing a Long-Range Interaction. SIAM Journal on Mathematical Analysis 37(4)
    [CrossRef]
  4. del Pino, Manuel (2007) Resonance and Interior Layers in an Inhomogeneous Phase Transition Model. SIAM Journal on Mathematical Analysis 38(5)
    [CrossRef]
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