Uniqueness of steady state, smooth shapes in a nonlocal geometric PDE
András Árpád Sipos · arXiv (Cornell University) · 2016
We investigate steady state solutions of a nonlocal geometric PDE that serves as a simple model of simultaneous contraction and growth of grains called ooids in geosciences. As a main result of the paper we demonstrate that the parameters associated with the physical environment determine a unique, steady state solution of the equation among smooth, convex curves embedded in $\mathbb{R}^2$. It is also revealed that any steady state solution possesses D2 symmetry.