Simultaneous determination of two coefficients in the Riemannian hyperbolic equation from boundary measurements

TL;DR

This paper addresses the inverse problem of simultaneously recovering the electric potential and absorption coefficient in a wave equation on a Riemannian manifold using boundary measurements, advancing understanding of boundary-based coefficient determination.

Contribution

It proves uniqueness results for the simultaneous determination of two coefficients in a wave equation from boundary data on Riemannian manifolds.

Findings

Uniqueness of coefficient recovery in dimensions n ≥ 2

Boundary measurements suffice for simultaneous determination

Extension of inverse boundary value problem theory

Abstract

In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential and the absorption coefficient 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 uni