A Degenerate Isoperimetric Problem and Traveling Waves to a Bistable Hamiltonian System. Issue 2 (22nd September 2015)

• Record Type: Journal Article
• Authors: Alama, Stan; Bronsard, Lia; Contreras, Andres; Dadok, Jiri; Sternberg, Peter
• Is Part Of: Communications on pure and applied mathematics. Volume 70:Issue 2(2017:Feb.)
• Page Start: 340
• Page End: 377
• Publication Date: 2015-09-22
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21615
• Languages: English
• ISSNs: 0010-3640

Abstract

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.