The purpose of this chapter is to provide a survey of our book by placing what we have to
say in a historical context. We obviously cannot give a complete account of inverse …

The field of inverse scattering theory has been a particularly active field in applied
mathematics for the past 25 years. The aim of research in this field has been to not only …

In the first edition of this book, we discussed methods for determining the support of an
inhomogeneous medium from measured far field data as well as an extensive study of the …

This survey aims to present the state of the art of research on the transmission eigenvalue
problem focussing on three main topics, namely the discreteness of transmission …

We consider the scattering of an acoustic plane wave by an inhomogeneous medium of
compact support. Our aim is to introduce a new class of target signatures that can be used to …

In this paper, we propose a conforming virtual element method for the Helmholtz
transmission eigenvalue problem of anisotropic media. By using 𝕋-coercivity theory, the …

We consider a surface integral formulation of the so-called interior transmission problem that
appears in the study of inverse scattering problems from dielectric inclusions. In the case …

In this paper we consider the transmission eigenvalue problem corresponding to the
scattering problem for an anisotropic magnetic materials with voids, ie subregions with …

We consider the inverse scattering problem for a cavity that is bounded by a penetrable
inhomogeneous medium of compact support and seek to determine the shape of the cavity …

The paper concerns the discreteness of the eigenvalues and the solvability of the interior
transmission problem for anisotropic media. Conditions for the ellipticity of the problem are …