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2019 Low regularity ray tracing for wave equations with Gaussian beams
Alden Waters
Rocky Mountain J. Math. 49(3): 1005-1027 (2019). DOI: 10.1216/RMJ-2019-49-3-1005

Abstract

We prove observability estimates for oscillatory Cauchy data modulo a small kernel for $n$-dimensional wave equations with space and time dependent $C^2$ and $C^{1,1}$ coefficients using Gaussian beams. We assume the domains and observability regions are in $\mathbb {R}^n$, and the GCC applies. This work generalizes previous observability estimates to higher dimensions and time dependent coefficients. The construction for the Gaussian beamlets solving $C^{1,1}$ wave equations represents an improvement and simplification over Waters (2011).

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Alden Waters. "Low regularity ray tracing for wave equations with Gaussian beams." Rocky Mountain J. Math. 49 (3) 1005 - 1027, 2019. https://doi.org/10.1216/RMJ-2019-49-3-1005

Information

Published: 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07088348
MathSciNet: MR3983312
Digital Object Identifier: 10.1216/RMJ-2019-49-3-1005

Subjects:
Primary: 35R01
Secondary: 35A22, 35L20, 35R30, 58J45

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 3 • 2019
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