JournalsifbVol. 3, No. 1pp. 45–80

Three-phase boundary motion by surface diffusion: stability of a mirror symmetric stationary solution

  • Katsuo Ito

    Kyushu University, Fukuoka, Japan
  • Yoshihito Kohsaka

    Hokkaido University, Sapporo, Japan
Three-phase boundary motion by surface diffusion: stability of a mirror symmetric stationary solution cover
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Abstract

We prove that the sharp interface model for a three-phase boundary motion by surface diffusion proposed by H. Garcke and A. Novick-Cohen admits a unique global solution provided the initial data fulfils a certain symmetric criterion and is also close to a minimizer of the energy under an area constraint. This minimizer is also a stationary solution of the present model. Moreover, we prove that the global solution converges to the minimizer of the energy as time goes to infinity.

Cite this article

Katsuo Ito, Yoshihito Kohsaka, Three-phase boundary motion by surface diffusion: stability of a mirror symmetric stationary solution. Interfaces Free Bound. 3 (2001), no. 1, pp. 45–80

DOI 10.4171/IFB/32