14:00 - 16:00, June 23, 2025 (Monday) Rm 21113, Department of Mathematics, NCUE
(彰化師範大學數學系 21113室)
Lamellar Critical Points of a Stationary Sharp Interface Model Yung-Sze Choi (University of Connecticut)
Abstract
Let be given positive constants and be a flat torus (with periodic boundary conditions). For any (measurable) set with a volume and perimeter (in BV sense) we study the geometric variational functional
where the nonlocal term is governed by in . Its corresponding Euler-Lagrange equation is
where is the mean curvature. This study differs from classical scenarios when we treat functions. We discuss technicality associated with this model.
The only known explicit solutions are (1D) planar lamellae with zero curvature. Their stability in various parameter regimes are analyzed. Details of a bifurcation analysis will be given; this leads to creation of non-planar solutions together with information on their stabilities.
