Stable Determination of the Discontinuous Conductivity Coefficient of a Parabolic Equation

TL;DR

This paper investigates how to stably identify a time-varying inclusion inside a thermal conductor using boundary measurements, establishing logarithmic stability estimates under certain regularity assumptions.

Contribution

It provides the first logarithmic stability estimates for the inverse problem of determining a discontinuous, time-varying conductivity within a parabolic equation.

Findings

Logarithmic stability estimates for the inverse problem.

Dependence of the inclusion on boundary data.

Conditions under which stability holds.

Abstract

We deal with the problem of determining a time varying inclusion within a thermal conductor. In particular we study the continuous dependance of the inclusion from the Dirichlet-to-Neumann map. Under a priori regularity assumptions on the unknown defect we establish logarithmic stability estimates.