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Long time existence of solutions to an elastic flow of networks

Garcke, Harald ; Menzel, Julia ; Pluda, Alessandra


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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