Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide

TL;DR

This paper establishes a logarithmic stability estimate for an inverse problem involving the heat equation in a waveguide, showing how to determine a spatially varying source factor from limited boundary measurements.

Contribution

It provides the first logarithmic stability result for the inverse source problem in an infinite waveguide setting for the heat equation.

Findings

Logarithmic stability estimate proved for the inverse source problem.

Unique determination of the source factor from a single boundary measurement.

Applicable to infinite waveguide geometries.

Abstract

We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with homogeneous initial and Dirichlet data.