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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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