Μάθημα : Σημειώσεις Μεταπτυχιακών μαθημάτων

Συντεταγμένες: Παρασκευή 08/11, ώρα 15.00, αίθουσα Α21 (ή κάποια άλλη από τις Α).

Ομιλητής: Zhiyuan Geng, University of Perdue, USA

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 minimising entire solution exhibiting a triple junction structure at infinity aling 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, we 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 interfaces.