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

Producción científica: Article › revisión exhaustiva

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	3801-3812
Número de páginas	12
Publicación	Proceedings of the American Mathematical Society
Volumen	149
N.º	9
DOI	https://doi.org/10.1090/proc/15460
Estado	Published - 2021

Nota bibliográfica

Publisher Copyright:
© 2021 American Mathematical Society

Financiación

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.

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	DMS-1708511
Australian Research Council	DP180100589
Simons Collaboration	586051

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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On the interaction of metric trapping and a boundary

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Nota bibliográfica

Financiación

ASJC Scopus subject areas

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