Long Time Existence of Solutions to an Elastic Flow of Networks
Analysis of PDEs
2019-01-29 v3
Abstract
The --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.
Cite
@article{arxiv.1901.03246,
title = {Long Time Existence of Solutions to an Elastic Flow of Networks},
author = {Harald Garcke and Julia Menzel and Alessandra Pluda},
journal= {arXiv preprint arXiv:1901.03246},
year = {2019}
}