In this paper, the problem of continuation of the solution of the ill-posed Cauchy problem for
matrix factorizations of the Helmholtz equation in a multidimensional bounded domain is …

In this paper, we present an explicit formula for the approximate solution of the Cauchy
problem for the matrix factorizations of the Helmholtz equation in a bounded domain on the …

Using our previous results, we show an explicit construction of the Carleman matrix for
matrix factorisations of the Helmholtz equation in an unbounded planar domain. This allows …

In the paper it is considered the problem of regularization of the Cauchy problem for matrix
factori-sations of the Helmholtz equation in three-dimensional unbounded domain. Using …

1 Department of Scientific Research, Innovation and Training of Scientific and Pedagogical
Staff, University of Economics and Pedagogy, IA Karimov 13, 180100, Karshi, Uzbekistan. e …

In the paper it is considered the regularization of the Cauchy problem for systems of elliptic
type equations of the first order with constant coefficients factorisable Helmholtz operator in …

The study delves into the persistent analysis and reliability assessment of the solution to the
Cauchy problem for the Helmholtz equation, within a defined area, using the known values …

It is known that the Cauchy problem for elliptic equations is unstable relatively small change
in the data, ie, is incorrect (Hadamard's example). In unstable problems the image of the …

This study aims to provide an understanding of well-posed and incorrectly-posed problems,
as well as the developed methods for solving incorrectly-posed applied problems in …

In this paper, we are talking about the Helmholtz equation and its physical meaning.
Helmholtz equation is used to solve problems in physics such as seismology …