Abstract

We model heterogeneous elastic wires by closed planar curves with density. The associated elastic energy depends on a density-modulated stiffness. Working with the inclination angle function, the $L^2$-gradient flow corresponding to this energy is a nonlocal quasilinear coupled parabolic system of second order. We show local well-posedness and global existence of solutions and study properties of the flow.

This talk is based on a joint work with Anna Dall’Acqua, Gaspard Jankowiak and Fabian Rupp.