## On the interaction of metric trapping and a boundary

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- by Kiril Datchev, Jason Metcalfe, Jacob Shapiro and Mihai Tohaneanu PDF
- Proc. Amer. Math. Soc.
**149**(2021), 3801-3812 Request permission

## 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.## References

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## Additional Information

**Kiril Datchev**- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
- MR Author ID: 860651
- Email: kdatchev@purdue.edu
**Jason Metcalfe**- Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
- MR Author ID: 733199
- Email: metcalfe@email.unc.edu
**Jacob Shapiro**- Affiliation: Mathematical Sciences Institute, Australian National University, Acton, Australian Capital Territory 2601, Australia; and Department of Mathematics, University of Dayton, Dayton, Ohio 45469-2316
- MR Author ID: 1311637
- Email: jshapiro1@udayton.edu
**Mihai Tohaneanu**- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
- MR Author ID: 886902
- Email: mihai.tohaneanu@uky.edu
- Received by editor(s): August 13, 2020
- Received by editor(s) in revised form: December 1, 2020
- Published electronically: June 4, 2021
- Additional Notes: 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.
- Communicated by: Ryan Hynd
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 3801-3812 - MSC (2020): Primary 35R01; Secondary 35B45
- DOI: https://doi.org/10.1090/proc/15460
- MathSciNet review: 4291579