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

Mathematics

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
State	Published - 2021

Bibliographical note

Funding Information:
Received by the editors August 13, 2020, and, in revised form, December 1, 2020. 2020 Mathematics Subject Classification. Primary 35R01; Secondary 35B45. The first author was supported in part by NSF grant DMS-1708511, the third author was supported in part by the Australian Research Council through grant DP180100589, and the fourth author was supported in part by Simons Collaboration Grant 586051.

Publisher Copyright:
© 2021 American Mathematical Society

ASJC Scopus subject areas

Mathematics (all)
Applied Mathematics

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AU - Shapiro, Jacob

AU - Tohaneanu, Mihai

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PY - 2021

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N2 - 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.

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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On the interaction of metric trapping and a boundary

Abstract

Bibliographical note

ASJC Scopus subject areas

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