Uniqueness of steady state, smooth shapes in a nonlocal geometric PDE and a model for the shape evolution of ooids

2017. 03. 02. 10:15
Sipos András Árpád

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 talk I demonstrate that the parameters associated with the physical environment determine a unique, time-invariant (equilibrium) solution of the equation among smooth, convex curves embedded in $\mathbb{R}^2$. The model produces nontrivial shapes that are consistent with recorded shapes of mature ooids found in nature.