Global existence for a non-local mean curvature flow as a limit of a parabolic-elliptic phase transition model | Zendy

Dorothea Hilhorst | Zendy; Elisabeth Logak | Zendy; Reiner Schätzle | Zendy

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Global existence for a non-local mean curvature flow as a limit of a parabolic-elliptic phase transition model

Author(s) -

Dorothea Hilhorst,

Elisabeth Logak,

Reiner Schätzle

Publication year - 2000

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/20

Subject(s) - gravitational singularity , mean curvature flow , limit (mathematics) , mean curvature , curvature , mathematics , diffusion , convergence (economics) , mathematical analysis , boundary (topology) , reaction–diffusion system , interval (graph theory) , phase transition , term (time) , flow (mathematics) , physics , geometry , thermodynamics , combinatorics , economics , economic growth , quantum mechanics

We consider a free boundary problem where the velocity depends on the mean curvature and on some non-local term. This problem arises as the singular limit of a reaction–diffusion system which describes the microphase separation of diblock copolymers. The interface may present singularities in finite time. This leads us to consider weak solutions on an arbitrary time interval and to prove the global-in-time convergence of solutions of the reaction–diffusion system.

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