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Long Time Existence of Solutions to an Elastic Flow of Networks

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arxiv 1901.03246 v3 pith:JN4IBH7Z submitted 2019-01-10 math.AP

Harald Garcke , Julia Menzel , Alessandra Pluda This is my paper · ORCID
classification math.AP
keywords existenceelasticflownetworkstimeboundaryconditionsenergy
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abstract

The $L^2$--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.

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