Asymptotic Analysis of Models for Geometric Motions
Dr. Gavin Glenn
Abstract:
We consider two problems related to the motion of hyper surfaces and curves by a normal velocity which depends on geometric quantities, such as curvature. We start by introducing these so-called Geometric Motions from the perspective of gradient flows of a surface energy. This leads to a nonlinear parabolic differential equation in local coordinates.
The first problem we consider is the singular pinch-off phenomenon for a tubular surface moving by Surface Diffusion. We prove the existence of a one-parameter family of pinching profiles obeying a long wavelength approximation of the dynamics.
For the second problem, we introduce a diffusion-based numerical scheme for Curve Shortening Flow. We prove that the scheme is one time-step consistent.
This part of the talk is joint work with Aaron Yip (Purdue).
Speaker’s Bio:
Gavin Glenn is an Associate Research Staff Member in the Cyber Resilience and Intelligence Division at the Oak Ridge National Lab. His research interests are in pure and applied differential equations, with some overlap in data sciences. He received his Ph.D. in Mathematics from Purdue University.
