Pyramidal traveling fronts in the Allen-Cahn equations (Viscosity Solutions of Differential Equations and Related Topics)
Masaharu Taniguchi · Kyoto University Research Information Repository (Kyoto University) · 2009
Pyramidal traveling fronts in the Allen-Cahn equations have been studied in the three-dimensional whole space.For a given admissible pyramid a pyramidal traveling front is uniquely deter- mined and it is asymptotically stable under the condition that given perturbations decay at infinity.A pyramidal traveling front is a combination of planar fronts on the lateral surfaces.Also it is a combination of two-dimensional V-form waves associated with the edges of a pyramid.