THE SURFACE-DIFFUSION FLOW FOR IMMERSED HYPERSURFACES

Authors
ESCHER J MAYER UF SIMONETT G
Citation
J. Escher et al., THE SURFACE-DIFFUSION FLOW FOR IMMERSED HYPERSURFACES, SIAM journal on mathematical analysis (Print), 29(6), 1998, pp. 1419-1433
Citations number
30
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on mathematical analysis (Print) → ACNP
ISSN journal
00361410
Volume
29
Issue
6
Year of publication
1998
Pages
1419 - 1433
Database
ISI
SICI code
0036-1410(1998)29:6<1419:TSFFIH>2.0.ZU;2-C
Abstract
We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a sphere, we prove that the solution exists globally and converges exponentially fast to a sphere. Further more, we provide numerical simulations showing the creation of singula rities for immersed curves.