Uniqueness of time-dependent inclusions in anisotropic heat conductive bodies

TL;DR

This paper proves the uniqueness of identifying a moving inclusion within an anisotropic heat-conductive body using boundary measurements, advancing inverse problem theory for heat equations with nonsmooth coefficients.

Contribution

It introduces a dynamical probe method to establish the uniqueness of a moving inclusion in a nonhomogeneous anisotropic medium from boundary data.

Findings

Uniqueness of the moving inclusion is proven.

The method handles nonsmooth conductivity coefficients.

Boundary measurements suffice for identification.

Abstract

We consider an inverse boundary value problem for the heat equation with a nonsmooth coefficient of conductivity which models the displacement of a moving body inside a nonhomogeneous background. We prove the uniqueness of the moving inclusion from the knowledge of the Dirichlet-to-Neumann operator by using a dynamical probe method.