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 …

We consider an inverse problem for Laplace equation by recovering the boundary value on
an inaccessible part of a circle from an overdetermined data on an accessible part of that …

Abstract In Ben Belgacem and El Fekih (2005 On Cauchy's problem: I. A variational Steklov–
Poincaré theory Inverse Problems 21 1915–36), a new variational theory is introduced for …

In this paper, we are interested in the study of an inverse Cauchy problem governed by
Stokes equation. It consists in determining the fluid velocity and the flux over a part of the …

In this work, an inverse problem in linear elasticity is considered, it is about reconstructing
the unknown boundary conditions on a part of the boundary based on the other boundaries …

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 are interested by an alternating method for an inverse Cauchy problem. Our main results
of this paper consists in exhibiting local error indicators, based on a posteriori analysis, with …

We consider the inverse Cauchy problems for Laplace equation in simply and doubly
connected plane domains by recoverning the unknown boundary value on an inaccessible …

In this paper, we are interested in solving a Cauchy inverse problem in linear elasticity. For
this, we propose a new method based on Robin conditions on the inaccessible boundary …