This monograph is a valuable contribution to the highly topical and extremly productive field
of regularisation methods for inverse and ill-posed problems. The author is an internationally …

An answer to the ill-posedness degree issue of the Cauchy problem may be found in the
theory of kernel operators. The foundation of the proof is the Steklov–Poincaré approach …

Abstract In 1923 (Lectures on Cauchy's Problem in Linear PDEs (New York, 1953)), J
Hadamard considered a particular example to illustrate the ill-posedness of the Cauchy …

In this paper, we introduce a new version of the method of quasi-reversibility to solve the ill-
posed Cauchy problems for the Laplace's equation in the presence of noisy data. It enables …

In this paper we propose a new method to stabilize nonsymmetric indefinite problems. The
idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilized …

The authors propose and analyze a well-posed numerical scheme for a type of ill-posed
elliptic Cauchy problem by using a constrained minimization approach combined with the …

A finite-element method is proposed for the nonlinear inverse problem of estimating the
Robin coefficient in a stationary diffusion equation from boundary measurements of the …

We study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic
problems: data completion problems for Poisson's and heat equations. We define an …

This work deals with domain decomposition like methods for solving an inverse Cauchy
problem governed by Stokes equation. As it is well known, this problem is one of highly ill …

This work considers the Cauchy problem for a second order elliptic operator in a bounded
domain. A new quasi-reversibility approach is introduced for approximating the solution of …