Crystalline curvature flow of planar networks | Zendy

Giovanni Bellettini | Zendy; Milena Chermisi | Zendy; Matteo Novaga | Zendy

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Crystalline curvature flow of planar networks

Author(s) -

Giovanni Bellettini,

Milena Chermisi,

Matteo Novaga

Publication year - 2006

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/152

Subject(s) - uniqueness , flow (mathematics) , planar , curvature , triple junction , topology (electrical circuits) , anisotropy , arc (geometry) , collision , mathematics , mechanics , geometry , physics , mathematical analysis , computer science , combinatorics , optics , computer graphics (images) , optoelectronics , computer security

We consider the evolution of a polycrystalline material with three or more phases, in the presence of an even crystalline anisotropy. We analyze existence, uniqueness, regularity and stability of the flow. In particular, if the flow becomes unstable at a finite time, we prove that an additional segment ( or even an arc) at the triple junction may develop in order to decrease the energy and make the flow stable at subsequent times. We discuss some examples of collapsing situations that lead to changes of topology, such as the collision of two triple junctions.

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