Time-Dependent Polarization Tensors: Derivation of Asymptotic Expansions for the Transient Wave Equation

TL;DR

This paper introduces the concept of time-dependent polarization tensors for the Helmholtz equation to aid in reconstructing small acoustic inclusions, laying the groundwork for future detailed analysis.

Contribution

It proposes a novel theoretical framework for time-dependent polarization tensors in the context of the Helmholtz equation, advancing inverse problem methods.

Findings

Framework for reconstructing small acoustic inclusions

Introduction of time-dependent polarization tensors

Foundation for future detailed investigations

Abstract

This report aims at establishing a theoretical framework for dealing with the reconstruction problem of a small acoustic inclusion. The objective is to introduce the new concept of time-dependent polarization tensors for the Helmholtz equation, which will be fully investigated in a forthcoming work.