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| STRONA GŁÓWNA | NAPISZ DO NAS LIST | MAPA SERWISU | |
A direct method for solving mean
curvature flow of planar curves with an anisotropy and external force
Daniel ©evčovič
Institute of Applied Mathematics
Faculty of Mathematics, Physics
and Informatics
Comenius University, Bratislava
|
We study evolution of plane curves satisfying the geometric equation 
We follow the so-called direct approach in order to derive a governing system of partial differential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves. We prove local in time existence of a classical solution. The equations include a nontrivial tangential velocity functional yielding a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system in order to find a numerical solution for 2D isotropic and anisotropic plane curve evolution, interface motions in thermomechanics and medical image segmentation problems. |
This is a joint work with
Karol Mikula. A preprint is available at
www.iam.fmph.uniba.sk/institute/sevcovic
04.04.2002
