Ημερομηνία: Παρασκευη 8 Νοεμβρίου 2024
Ώρα: 15:00
Τόπος: Α22
Oμιλητής: Zhiyuan Geng, from the University of Purdue, US
Τίτλος: Uniqueness of the blow-down limit for the Allen-Cahn solution with a triple junction structure
Περίληψη: In this talk, we investigate the vector-valued Allen-Cahn system with a triple-well potential, motivated by recent works of Alikakos-Geng and Sandier-Sternberg, which establish the existence of a minimizing entire solution exhibiting a triple junction structure at infinity along certain subsequences. We prove the uniqueness of the blow-down limit for this solution using a variational approach. Central to our analysis is a precise estimation of the diffuse interface’s location and size, achieved through tight upper and lower energy bounds. Furthermore, I will present new results on the asymptotic flatness of the diffuse interface at infinity, revealing that the solution is nearly invariant along the direction of the sharp interface.