A Degenerate Isoperimetric Problem and Traveling Waves to a Bi-stable Hamiltonian System
Abstract
We analyze a non-standard 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 bi-stable Hamiltonian system of PDE's. We also determine the existence of a maximal propagation speed for these traveling waves through an explicit upper bound depending on the conformal factor.
Keywords
Cite
@article{arxiv.1504.00423,
title = {A Degenerate Isoperimetric Problem and Traveling Waves to a Bi-stable Hamiltonian System},
author = {Stan Alama and Lia Bronsard and Andres Contreras and Jiri Dadok and Peter Sternberg},
journal= {arXiv preprint arXiv:1504.00423},
year = {2015}
}
Comments
Subsection 3.1, concerning the existence of a minimizer in the two-well case, has been amended