Advances in Differential Equations

Willmore-type regularization of mean curvature flow in the presence of a non-convex anisotropy. The graph setting: analysis of the stationary case and numerics for the evolution problem

Paola Pozzi and Philipp Reiter

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Abstract

In this paper we investigate the motion of one-dimensional graphs under anisotropic non-convex mean curvature flow regularized via a Willmore term. Aiming at understanding the evolution problem when we let the regularization parameter tend to zero, we first present rigorous analytical results for the stationary case. Subsequently we discuss the time-dependent problem, focussing mainly on numerical simulations. We discretize by finite elements, and provide a semi-implicit scheme and a number of numerical experiments.

Article information

Source
Adv. Differential Equations Volume 18, Number 3/4 (2013), 265-308.

Dates
First available in Project Euclid: 5 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1360073018

Mathematical Reviews number (MathSciNet)
MR3060197

Zentralblatt MATH identifier
1273.35098

Subjects
Primary: 35G31: Initial-boundary value problems for nonlinear higher-order equations 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 35Q99: None of the above, but in this section

Citation

Pozzi, Paola; Reiter, Philipp. Willmore-type regularization of mean curvature flow in the presence of a non-convex anisotropy. The graph setting: analysis of the stationary case and numerics for the evolution problem. Adv. Differential Equations 18 (2013), no. 3/4, 265--308. https://projecteuclid.org/euclid.ade/1360073018.


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