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arXiv · 2205.06587

A dynamic approach to heterogeneous elastic wires

Anna Dall'Acqua·Leonie Langer·Fabian Rupp
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Abstract

We consider closed planar curves with fixed length and arbitrary winding number whose elastic energy depends on an additional density variable and a spontaneous curvature. Working with the inclination angle, the associated $L^2$-gradient flow is a nonlocal quasilinear coupled parabolic system of second order. We show local well-posedness, global existence of solutions, and full convergence of the flow for initial data in a weak regularity class.

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Anna Dall'Acqua, Leonie Langer, Fabian Rupp. 2022-05-13. A dynamic approach to heterogeneous elastic wires. https://doi.org/10.1016/j.jde.2024.02.001

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