Stability for a formally determined inverse problem for a hyperbolic PDE with space and time dependent coefficients

TL;DR

This paper establishes stability results for an inverse problem involving a hyperbolic PDE with space and time-dependent coefficients, using a modified Bukhgeim-Klibanov method, applicable in various spatial dimensions.

Contribution

It introduces a novel stability proof for a formally determined inverse problem with variable coefficients in hyperbolic PDEs, extending the Bukhgeim-Klibanov method.

Findings

Proves stability for inverse problems with space-time dependent coefficients

Applicable to hyperbolic PDEs with constant wave speed in multiple dimensions

Uses a modified Bukhgeim-Klibanov method for the analysis

Abstract

We prove stability for a formally determined inverse problem for a hyperbolic PDE where the coefficients depend on space and time variables. The hyperbolic operator has constant wave speed and we study the recovery of zeroth order and first order coefficients and the space dimension can be one or higher. We use a modification of the Bukhgeim-Klibanov method to obtain our results.