High order curvature flows of plane curves with generalised Neumann boundary conditions

Title: High order curvature flows of plane curves with generalised Neumann boundary conditions
Creator: McCoy, James; Wheeler, Glen; Wu, Yuhan
Relation: Advances in Calculus of Variations Vol. 15, Issue 3, p. 497-513
Publisher Link: http://dx.doi.org/10.1515/acv-2020-0002
Publisher: Walter de Gruyter GmbH
Resource Type: journal article
Date: 2022
Description: We consider the parabolic polyharmonic diffusion and the L 2-gradient flow for the square integral of the m-th arclength derivative of curvature for regular closed curves evolving with generalised Neumann boundary conditions. In the polyharmonic case, we prove that if the curvature of the initial curve is small in L 2, then the evolving curve converges exponentially in the C ∞ topology to a straight horizontal line segment. The same behaviour is shown for the L 2-gradient flow provided the energy of the initial curve is sufficiently small. In each case the smallness conditions depend only on m.
Subject: curvature flow; high order parabolic equation; Neumann boundary condition; conditions
Identifier: http://hdl.handle.net/1959.13/1452834
Identifier: uon:44515
Identifier: ISSN:1864-8258
Language: eng
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