Determination of small linear perturbations in the diffusion coefficient from partial dynamic boundary measurements

TL;DR

This paper presents a method to reconstruct small changes in heat conductivity within a medium using limited dynamic boundary data over time, employing control techniques and inverse Fourier transform analysis.

Contribution

It introduces a novel approach to identify small perturbations in the diffusion coefficient from partial boundary measurements in heat conduction problems.

Findings

Successfully reconstructs small perturbations from partial data

Provides a rigorous mathematical derivation of the inverse problem solution

Employs control methods and inverse Fourier transform for analysis

Abstract

This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary) dynamic boundary measurements and for finite interval in time. By constructing of appropriate test functions, using a control method, we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the diffusion coefficient as the leading order of an appropriate averaging of the partial dynamic boundary measurements.