The surface diffusion flow for immersed hypersurfaces

被引：107

作者：

Escher, J ^{[1
]}

Mayer, UF

Simonett, G

机构：

[1] Univ Basel, Inst Math, CH-4051 Basel, Switzerland

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1998年 / 29卷 / 06期

关键词：

surface diffusion; mean curvature; free boundary problem; immersed hypersurfaces; center manifolds; maximal regularity; numerical simulations;

D O I：

10.1137/S0036141097320675

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. Furthermore, we provide numerical simulations showing the creation of singularities for immersed curves.

引用

页码：1419 / 1433

页数：15

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