A Degenerate Isoperimetric Problem and Traveling Waves to a Bi-stable\n Hamiltonian System

2015/04/01 by Stan Alama, Alama, Stan, Lia Bronsard +7 · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1504.00423

openalex publication_date 2015/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze a non-standard isoperimetric problem in the plane associated with\na metric having degenerate conformal factor at two points. Under certain\nassumptions on the conformal factor, we establish the existence of curves of\nleast length under a constraint associated with enclosed Euclidean area. As a\nmotivation for and application of this isoperimetric problem, we identify these\nisoperimetric curves, appropriately parametrized, as traveling wave solutions\nto a bi-stable Hamiltonian system of PDE's. We also determine the existence of\na maximal propagation speed for these traveling waves through an explicit upper\nbound depending on the conformal factor.\n

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