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

Katsuo Ito | Zendy; Yoshihito Kohsaka | Zendy

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

Author(s) -

Katsuo Ito,

Yoshihito Kohsaka

Publication year - 2001

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/32

Subject(s) - boundary (topology) , mathematics , motion (physics) , infinity , constraint (computer aided design) , mathematical analysis , surface (topology) , diffusion , phase (matter) , stability (learning theory) , surface energy , classical mechanics , physics , geometry , computer science , thermodynamics , quantum mechanics , machine learning

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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