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.
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页码：1253 / 1305
页数：53
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