Stable recovery of a metric tensor from the partial hyperbolic Dirichlet to Neumann map

Mourad Bellassoued

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arXiv · 2101.02955

Stable recovery of a metric tensor from the partial hyperbolic Dirichlet to Neumann map

Mourad Bellassoued

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Abstract

In this paper we consider the inverse problem of determining on a compact Riemannian manifold the metric tensor in the wave equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\geq 2$ that the knowledge of the Dirichlet-to-Neumann map for the wave equation uniquely determines the metric tensor and we establish logarithm-type stability.

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Mourad Bellassoued. 2021-01-08. Stable recovery of a metric tensor from the partial hyperbolic Dirichlet to Neumann map. https://arxiv.org/abs/2101.02955

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