A Degenerate Isoperimetric Problem and Traveling Waves to a Bistable Hamiltonian System. Issue 2 (22nd September 2015) - Alama, Stan; Bronsard, Lia; Contreras, Andres; Dadok, Jiri; Sternberg, Peter
Abstract : We analyze a nonstandard isoperimetric problem in the plane associated with a metric having degenerate conformal factor at two points. Under certain assumptions on the conformal factor, we establish the existence of curves of least length under a constraint associated with enclosed euclidean area. As a motivation for and application of this isoperimetric problem, we identify these isoperimetric curves, appropriately parametrized, as traveling wave solutions to a bistable Hamiltonian system of PDEs. We also determine the existence of a maximal propagation speed for these traveling waves through an explicit upper bound depending on the conformal factor.© 2015 Wiley Periodicals, Inc.