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

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.

This report introduces the mathematical framework for dealing with the reconstruction problem of a small acoustic inclusion fully developed in arXiv:2003.09806 and thus has been withdrawn by the author. In arXiv:2003.09806, which has to be intended as a revised extension of arXiv:1903.10814, typos regarding the 2D case have been corrected