The theory of reproducing kernels started with two papers of 1921 [449] and 1922 [45] which
dealt with typical reproducing kernels of Szegö and Bergman, and since then the theory has …

Radial Basis Function (RBF) methods have become the primary tool for interpolating
multidimensional scattered data. RBF methods also have become important tools for solving …

In this paper we combine the method of fundamental solutions with various regularization
techniques to solve Cauchy problems of elliptic differential operators. The main idea is to …

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 …

The study deals with the heat and mass transfer process near the dynamic three-phase
liquid–gas–solid contact line. The evaporating sessile water droplets on a horizontal heated …

In this paper, we examine the Cauchy problem of the Laplace equation. Motivated by the
incompleteness of the single-layer potential function method, we investigate the double …

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 propose an approximate optimal control formulation of the Cauchy
problem, for an elliptic equation, equivalent to the original one under some regularity …

A new method is described for the problem of expanding known displacement fields at the
boundary of a solid together with the surface tractions on it, towards the solid interior up to …

A novel artificial neural network method is proposed for solving Cauchy inverse problems.
Using multiple-layers network as an approximation we present a non-mesh discretization to …