科研之友
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摘要
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.
- 出版日期2017-2
