A dynamic approach to heterogeneous elastic wires

Abstract

We consider closed planar curves with fixed length 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 and global existence of solutions for initial data in a weak regularity class and with arbitrary winding number.