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 …

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 …

This work is a survey of results for ill-posed Cauchy problems for PDEs of the author with co-
authors starting from 1991. A universal method of the regularization of these problems is …

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 …

The coefficient inverse problem for the two-dimensional wave equation is solved. We apply
the Gelfand–Levitan approach to transform the nonlinear inverse problem to a family of …

A new domain decomposition method for Maxwell's equations in conductive media is
presented. Using this method, reconstruction algorithms are developed for the determination …

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 paper investigates the inverse problem of determining the time-dependent heat source
and the temperature for the heat equation with a non-classical boundary and an integral …

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 …

We consider the problem of imaging of objects buried under the ground using experimental
backscattering time-dependent measurements generated by a single point source or one …