A dynamic approach to heterogeneous elastic wires

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.

arXiv comment31 pages. New version includes proof of full convergence. Comments are welcome!

References in corpus (6)

• The Łojasiewicz-Simon gradient inequality for open elastic curves
• A survey of the elastic flow of curves and networks
• On the Lojasiewicz-Simon gradient inequality on submanifolds
• The volume-preserving Willmore flow
• The Willmore flow with prescribed isoperimetric ratio
• Elliptic operators and maximal regularity on periodic little-Hölder spaces

Cited by in corpus (1)

• Conservation, convergence, and computation for evolving heterogeneous elastic wires