On the interaction of metric trapping and a boundary
Analysis of PDEs
2021-08-13 v2
Abstract
By considering a two ended warped product manifold, we demonstrate a bifurcation that can occur when metric trapping interacts with a boundary. In this highly symmetric example, as the boundary passes through the trapped set, one goes from a nontrapping scenario where lossless local energy estimates are available for the wave equation to the case of stably trapped rays where all but a logarithmic amount of decay is lost.
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Cite
@article{arxiv.2008.05408,
title = {On the interaction of metric trapping and a boundary},
author = {Kiril Datchev and Jason Metcalfe and Jacob Shapiro and Mihai Tohaneanu},
journal= {arXiv preprint arXiv:2008.05408},
year = {2021}
}
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12 pages