The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a
subject in which its creator takes a keen interest. The concept of ill-posed problems was …

В учебном пособии изложены методы исследования и решения обратных и
некорректных задач линейной алгебры, интегральных и операторных уравнений …

Driven by the advancement of industrial mathematics and the need for impact case studies,
Inverse Problems with Applications in Science and Engineering thoroughly examines the …

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 …

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 …

This paper studies a non‐linear inverse problem associated with the Laplace equation of
identifying the Robin coefficient from boundary measurements. A variational formulation of …

The Cauchy problem for the Helmholtz equation appears in various applications. The
problem is severely ill-posed and regularization is needed to obtain accurate solutions. We …

In the framework of stationary anisotropic heat conduction (the Laplace-Beltrami equation)
without heat sources, we investigate both theoretically and numerically the acceleration of …

We consider the Cauchy problem for the Laplace equation, ie the reconstruction of a
harmonic function from knowledge of the value of the function and its normal derivative …

We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One
method to approximate the solution associated with compatible data consists in considering …