PDE seminar: An $(N-1)$-dimensional strictly convex compact set gives an $N$-dimensional traveling front in the Allen-Cahn equation

2013-11-13 16:30 - 2013-11-13 17:30
Faculty of Science Building #3, Room 309
Masaharu Taniguchi (Okayama University)
The Allen-Cahn equation is a simple example for reactiondiffusion
equations with bistable nonlinearity. For this
equation, the existence and stability of two-dimensional
V-form fronts are proved by Ninomiya and T(2005). $N$-
dimensional cylindrically symmetric traveling fronts are
studied by Hamel, Monneau and Roquejoffre(2005, 2006)
and Chen, Guo, Ninomiya, Hamel, Roquejoffre(2007).
Traveling fronts of pyramidal shapes are studied by T
(2007) and Kurokawa-T(2011). In this talk I will explain
my recent work and show that there exists an $N$-
dimensional traveling front associated with an $(N-1)$-
dimensional strictly convex compact set.