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Low regularity ray tracing for wave equations with Gaussian beams. (English) Zbl 1418.35349

Summary: 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 A. Waters [Commun. Math. Sci. 9, No. 1, 225–254 (2011; Zbl 1295.35011)].

MSC:

35R01 PDEs on manifolds
35R30 Inverse problems for PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
58J45 Hyperbolic equations on manifolds
35A22 Transform methods (e.g., integral transforms) applied to PDEs

Citations:

Zbl 1295.35011
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References:

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