This book summarizes the main analytical and numerical results of Carleman estimates. In
the analytical part, Carleman estimates for three main types of Partial Differential Equations …

We present in this paper a novel numerical reconstruction method for solving a three-
dimensional inverse scattering problem with scattering data generated by a single direction …

For the first time, we develop in this paper the globally convergent convexification numerical
method for a coefficient inverse problem for the three-dimensional Helmholtz equation for …

By our definition,“restricted Dirichlet-to-Neumann (DN) map” means that the Dirichlet and
Neumann boundary data for a coefficient inverse problem (CIP) are generated by a point …

A version of the so-called “convexification” numerical method for a coefficient inverse
scattering problem for the 3D Helmholtz equation is developed analytically and tested …

This work is concerned with the inverse source problem of locating multiple multipolar
sources from boundary measurements for the Helmholtz equation. We develop simple and …

A new numerical method is proposed for a one-dimensional inverse medium scattering
problem with multifrequency data. This method is based on the construction of a weighted …

The goal of this paper is to develop a globally convergent numerical method for the inverse
problem which would work with the optical experimental data collected by this research …

We present a reconstruction method for solving a 3D coefficient inverse problem with a
single measurement of phaseless scattering data. These are multifrequency data generated …

This paper is concerned with the numerical solution to a three-dimensional coefficient
inverse problem for buried objects with multi-frequency experimental data. The measured …