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arXiv · 2008.05408

On the interaction of metric trapping and a boundary

Kiril Datchev·Jason Metcalfe·Jacob Shapiro·Mihai Tohaneanu
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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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Kiril Datchev, Jason Metcalfe, Jacob Shapiro, Mihai Tohaneanu. 2020-08-12. On the interaction of metric trapping and a boundary. https://arxiv.org/abs/2008.05408

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