On the interaction of metric trapping and a boundary

Kiril Datchev; Jason Metcalfe; Jacob Shapiro; Mihai Tohaneanu

doi:10.1090/proc/15460

On the interaction of metric trapping and a boundary

Kiril Datchev, Jason Metcalfe, Jacob Shapiro, Mihai Tohaneanu

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3801-3812
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	9
DOIs	https://doi.org/10.1090/proc/15460
Publication status	Published - 2021

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title = "On the interaction of metric trapping and a boundary",

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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AU - Shapiro, Jacob

AU - Tohaneanu, Mihai

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AB - 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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U2 - 10.1090/proc/15460

DO - 10.1090/proc/15460

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SP - 3801

EP - 3812

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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On the interaction of metric trapping and a boundary

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