Long time existence of solutions to an elastic flow of networks

DOI10.1080/03605302.2020.1771364zbMath1460.35036arXiv1901.03246OpenAlexW3033178824MaRDI QIDQ4966060

Alessandra Pluda, Julia Menzel, Harald Garcke

Publication date: 18 March 2021

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.03246

zbMATH Keywords

geometric evolution equationsWillmore flowparabolic system of fourth order

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Initial-boundary value problems for higher-order parabolic systems (35K52) PDEs on graphs and networks (ramified or polygonal spaces) (35R02) Flows related to mean curvature (53E10)

Related Items (11)

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 ⋮ On the convergence of the Willmore flow with Dirichlet boundary conditions ⋮ Convergence of elastic flows of curves into manifolds ⋮ Elastic networks, statics and dynamics ⋮ Elastic flow of networks: short-time existence result ⋮ A survey of the elastic flow of curves and networks ⋮ Degenerate elastic networks ⋮ Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds

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