Long Time Existence of Solutions to an Elastic Flow of Networks

2019/01/10 by Harald Garcke, Garcke, Harald, Julia Menzel +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1901.03246

arxiv created 2019/01/28 · arxiv updated 2019/01/29

Abstract

The L²--gradient flow of the elastic energy of networks leads to a Willmore type evolution law with nontrivial 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.

Related

• Flow of elastic networks: long-time existence result
• Willmore Flow of planar networks
• Elastic flow of curves with partial free boundary
• Short-time existence for the network flow
• Short‐time existence for the network flow