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 …

Inverse scattering problems of the reconstructions of physical properties of a medium from
boundary measurements are substantially challenging ones. This work aims to verify the …

This is a continuation of two recent publications of the authors [J. Inverse Ill-Posed Probl., 23
(2015), pp. 415--426; J. Inverse Ill-Posed Probl., 23 (2015), pp. 187--193] about …

In this paper, a new asymptotic-numerical approach to solving an inverse boundary value
problem for a nonlinear singularly perturbed parabolic equation with time-periodic …

This report extends our recent progress in tackling a challenging 3D inverse scattering
problem governed by the Helmholtz equation. Our target application is to reconstruct …

The 3D inverse scattering problem of the reconstruction of the unknown dielectric permittivity
in the generalized Helmholtz equation is considered. Applications are in imaging of …

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 …

One way of improving the behavior of finite element schemes for classical, time-dependent
Maxwell's equations is to render their hyperbolic character to elliptic form. This paper is …

This article develops the numerical and theoretical study of the reconstruction algorithm of a
potential in a wave equation from boundary measurements, using a cost functional built on …

arXiv:1607.03978v1 [math-ph] 14 Jul 2016 Page 1 arXiv:1607.03978v1 [math-ph] 14 Jul 2016
Uniqueness of a phaseless inverse scattering problem for the generalized 3-D Helmholtz …