Willmore flow of planar networks

DOI10.1016/j.jde.2018.08.019zbMath1436.35233arXiv1711.11504OpenAlexW2964093025MaRDI QIDQ2423240

Julia Menzel, Alessandra Pluda, Harald Garcke

Publication date: 21 June 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.11504

zbMATH Keywords

junctionsnetworksgeometric evolution equationsWillmore flowparabolic systems of fourth order

Mathematics Subject Classification ID

PDEs in connection with mechanics of deformable solids (35Q74) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Higher-order parabolic systems (35K41) Initial-boundary value problems for higher-order parabolic systems (35K52) Higher-order geometric flows (53E40)

Related Items (15)

A regularized gradient flow for the \(p\)-elastic energy ⋮ Curve-shortening of open elastic curves with repelling endpoints: a minimizing movements approach ⋮ Existence and uniqueness of the motion by curvature of regular networks ⋮ Overdamped dynamics of a falling inextensible network: existence of solutions ⋮ Li-Yau type inequality for curves in any codimension ⋮ Convergence of elastic flows of curves into manifolds ⋮ Elastic flow of networks: long-time existence result ⋮ On the surface diffusion flow with triple junctions in higher space dimensions ⋮ Elastic networks, statics and dynamics ⋮ Elastic flow of networks: short-time existence result ⋮ A survey of the elastic flow of curves and networks ⋮ Long time existence of solutions to an elastic flow of networks ⋮ Degenerate elastic networks ⋮ A Second Order Gradient Flow of p-Elastic Planar Networks ⋮ Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds

Cites Work

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• Minimal elastic networks
• ELASTIC FLOW WITH JUNCTIONS: VARIATIONAL APPROXIMATION AND APPLICATIONS TO NONLINEAR SPLINES
• On the Solvability of Free Boundary Problem for Viscous Compressible Fluids in an Infinite Time Interval
• Short time existence for the elastic flow of clamped curves
• Analytic semigroups and optimal regularity in parabolic problems
• A singular limit for a system of degenerate Cahn-Hilliard equations

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