# The role and essence of ill-posed problems for solving various applied problems

## Keywords:

Ill-posed problems, Carleman function, Helmholtz equation, Approximate solution, Cauchy problem## Abstract

In this paper, the history of the appearance of ill-posed problems and the role and essence of these problems in solving various problems of equations of mathematical physics are described in detail. At the present time, the theory and application of ill-posed problems in various fields of science is rapidly developing. When solving ill-posed problems, we will construct a Carleman function and, on its basis, we will find in an explicit form an approximate solution of the problem.

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