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

Abstract: In this talk 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 sub-boundary observations. This information is enclosed in the dynamical partial Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\geq 2$ that the knowledge of the partial Dirichlet-to-Neumann map for the wave equation uniquely determines the metric tensor and we establish logarithm-type stability.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine