Stability estimate for a partial data inverse problem for the convection-diffusion equation

TL;DR

This paper establishes stability estimates for an inverse problem involving the convection-diffusion equation, showing log-log stability for the convection term and log-log-log stability for the density coefficient from partial boundary data.

Contribution

It provides the first stability estimates for the inverse problem of determining both convection and density coefficients from partial boundary measurements.

Findings

Log-log stability for the convection term (modulo gauge)

Log-log-log stability for the density coefficient

Stability estimates derived for dimensions n ≥ 2

Abstract

In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension $n\geq 2$, we show the convection term (modulo the gauge term) admits log-log stability, whereas log-log-log stability estimate is obtained for the density coefficient.