Journal article
Curvature-Driven Flows: A Variational Approach
SIAM journal on control and optimization, Vol.31(2), pp.387-438
03/1993
DOI: 10.1137/0331020
Abstract
This paper introduces a new mathematical approach to the study of time evolutions of solids $K(t)$ in n-space whose boundaries move with velocity equal to the weighted mean curvature derived from the boundary surface energy $\Phi (\partial K(t))$. These “flat $\Phi $ curvature flows” are limits of sequences of solutions to variational problems in which a sum of surface and bulk energy is minimized. The construction works equally well for smooth elliptic $\Phi $’s, for nondifferentiable crystalline $\Phi $’s, and for anything in between. The flows agree with classical smooth flows when the data is smooth and elliptic in any dimension and coincide with motion by crystalline curvature for polyhedral curves in the plane.
Details
- Title: Subtitle
- Curvature-Driven Flows: A Variational Approach
- Creators
- Fred AlmgrenJean E TaylorLihe Wang - University of Iowa, Mathematics
- Resource Type
- Journal article
- Publication Details
- SIAM journal on control and optimization, Vol.31(2), pp.387-438
- DOI
- 10.1137/0331020
- ISSN
- 0363-0129
- eISSN
- 1095-7138
- Language
- English
- Date published
- 03/1993
- Academic Unit
- Mathematics
- Record Identifier
- 9984206855402771
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