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.
|Number of pages||12|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - 2021|
Bibliographical noteFunding 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.
© 2021 American Mathematical Society
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics