Linear sampling method for identifying cavities in a heat conductor

TL;DR

This paper introduces a linear sampling method for detecting cavities in heat conductors using boundary data, leveraging the flexibility of time variable choice to enhance data utilization.

Contribution

It develops a novel linear sampling approach for the heat equation that exploits time variable freedom, extending inverse boundary problem techniques.

Findings

Effective identification of cavities demonstrated.

Utilizes additional data from time variable flexibility.

Applicable to inverse heat conduction problems.

Abstract

We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a freedom to choose the time variable, which suggests that we have more data than the linear sampling methods for the inverse boundary value problem associated with EIT and inverse scattering problem with near field data.