Long time existence of solutions to an elastic flow of networks
Harald Garcke, Julia Menzel, Alessandra Pluda
2020CINECA IRIS Institutial research information system (University of Pisa)20 citationsDOIOpen Access PDF
Abstract
The L2-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.
Topics & Concepts
UniquenessMathematicsSobolev spaceBalanced flowFlow (mathematics)Mathematical analysisNonlinear systemType (biology)Boundary (topology)Boundary value problemGeometryPhysicsQuantum mechanicsEcologyBiologyAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsGeometric Analysis and Curvature Flows