A nonlinear partial differential equation for the volume preserving mean curvature flow | Zendy

Dimitra C. Antonopoulou | Zendy; Georgia Karali | Zendy

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A nonlinear partial differential equation for the volume preserving mean curvature flow

Author(s) -

Dimitra C. Antonopoulou,

Georgia Karali

Publication year - 2013

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2013.8.9

Subject(s) - mean curvature flow , partial differential equation , curvature , flow (mathematics) , regular polygon , mathematics , mean curvature , nonlinear system , finite volume method , mathematical analysis , plane (geometry) , geometry , mechanics , physics , quantum mechanics

We analyze the evolution of multi-dimensional normal graphs over the unit sphere under volume preserving mean curvature flow and derive a non-linear partial differential equation in polar coordinates. Furthermore, we construct finite difference numerical schemes and present numerical results for the evolution of non-convex closed plane curves under this flow, to observe that they become convex very fast.

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