Relaxation of the flow of triods by Curve Shortening Flow via the vector-valued parabolic Allen-Cahn equation

Abstract

In this paper we find solutions $u_{\epsilon }$ to a certain class of vector-valued parabolic Allen-Cahn equation that as $\epsilon \to 0$ develops as interface a given triod evolving under curve shortening flow.

20 pages, 2 figures

References in corpus (1)

• Existence of a solution to a vector-valued Allen-Cahn equation with a three well potential