Stable determination outside a cloaking region of two time-dependent coefficients in an hyperbolic equation from Dirichlet to Neumann map

TL;DR

This paper addresses the inverse problem of stably recovering two time-dependent coefficients in a hyperbolic PDE from boundary measurements, even in the presence of cloaking regions, by establishing stability estimates and data enlargement techniques.

Contribution

It introduces stability estimates for determining coefficients outside cloaking regions and demonstrates stable recovery in larger domains through data extension.

Findings

Stability estimates for coefficients outside cloaking regions.

Stable recovery of coefficients in larger domains with extended data.

Applicable in dimensions n ≥ 2.

Abstract

In this paper, we treat the inverse problem of determining two time-dependent coefficients appearing in a dissipative wave equation, from measured Neumann boundary observations. We establish in dimension $n\geq 2$, stability estimates with respect to the Dirichlet-to-Neumann map of these coefficients provided that are known outside a cloaking regions. Moreover, we prove that it can be stably recovered in larger subsets of the domain by enlarging the set of data