A degenerate isoperimetric problems and traveling waves to a bi-stable Hamiltonian system

We analyze a non-standard isoperimetric problem in the plane associated with a metric having degenerate conformal factor at two points. Under certain assump- tions 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 isoperimet- ric 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 de- pending on the conformal factor.


Publication Date:
Sep 22 2015
Date Submitted:
Nov 30 2018
ISSN:
1097-0312
Citation:
Communications on Pure and Applied Mathematics
70
2

Note: The status of this file is: public



 Record created 2018-11-30, last modified 2019-04-03

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