English

Long Time Existence of Solutions to an Elastic Flow of Networks

Analysis of PDEs 2019-01-29 v3

Abstract

The L2L^2--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.

Keywords

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}
}