Work

Dynamics of elastic wires: preserving area without nonlocality

Year: 2025

Type: article

Abstract: We derive an $$H^{-1}$$ H - 1 -gradient flow of the elastic energy which preserves the enclosed area of evolving planar curves. For this new sixth-order evolution equation, we prove a global existence result. Additionally, by penalizing the length, we show convergence to an area constrained critical point of the elastic energy.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-02948-0

Author: Leonie Langer

Institution: Universität Ulm

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Universität Ulm