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

Zbl 1295.35011
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