Long time existence of solutions to an elastic flow of networks

被引：13

作者：

Garcke, Harald ^{[1
]}

Menzel, Julia ^{[1
]}

Pluda, Alessandra ^{[2
]}

机构：

[1] Univ Regensburg, Fak Math, Regensburg, Germany

[2] Univ Pisa, Dipartimento Matemat, Lgo B Pontecorvo 5, I-56125 Pisa, Italy

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 45卷 / 10期

关键词：

Geometric evolution equations; networks; parabolic system of fourth order; Willmore flow; Primary; Secondary; TRIPLE JUNCTIONS; CURVATURE; CURVES; MOTION; EVOLUTION; L-2-FLOW;

D O I：

10.1080/03605302.2020.1771364

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

TheL(2)-gradient flow of the elastic energy of networks leads to a Willmore type evolution law with non-trivial nonlinear boundary conditions. We show local in time existence and uniqueness for this elastic flow of networks in a Sobolev space setting under natural boundary conditions. In addition, we show a regularisation property and geometric existence and uniqueness. The main result is a long time existence result using energy methods.

引用

页码：1253 / 1305

页数：53

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