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arXiv · 2101.10740

Counterexamples to inverse problems for the wave equation

Tony Liimatainen·Lauri Oksanen
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Abstract

We construct counterexamples to inverse problems for the wave operator on domains in $\mathbb{R}^{n+1}$, $n \ge 2$, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which are formulated in terms certain restrictions of the Dirichlet-to-Neumann map. The Lorentzian metrics giving counterexamples are time-dependent, but they are smooth and non-degenerate. On $\mathbb{R}^{n+1}$ the metrics are conformal to the Minkowski metric.

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Tony Liimatainen, Lauri Oksanen. 2021-01-26. Counterexamples to inverse problems for the wave equation. https://arxiv.org/abs/2101.10740

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