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Low regularity ray tracing for wave equations with Gaussian beams

Waters, A., 2019, In : Rocky mountain journal of mathematics. 49, 3, p. 1005-1027 23 p.

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  • Low regularity ray tracing for wave equations with Gaussian beams

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DOI

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,C-1 coefficients using Gaussian beams. We assume the domains and observability regions are in 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,C-1 wave equations represents an improvement and simplification over Waters (2011).

Original languageEnglish
Pages (from-to)1005-1027
Number of pages23
JournalRocky mountain journal of mathematics
Volume49
Issue number3
Publication statusPublished - 2019

    Keywords

  • Control theory, inverse problems, wave equations, observability, low regularity coefficients, Gaussian beams, STABLE DETERMINATION, STABILITY, TRANSFORMS, UNIQUENESS

ID: 101127788