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.
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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. 45–80DOI 10.4171/IFB/32