Inverse, ill-posed problems, essentially different solutions and explicit formulas for solutions

Author:

Demidov A.S.

Abstract

Abstract A request for an inverse problem, as well as for an incorrect problem produces tens of millions of answers in the Internet. In the past few decades, hundreds of international conferences on these topics have been held annually. Problems of this kind are quite involved, and their numerical analysis requires the development of special methods and numerical algorithms. Explicit formulas provide the main tool for testing these methods and numerical algorithms. The Cauchy problem for an elliptic equation is a classical ill-posed problem, which serves as a model for many inverse and incorrect problems. In the present paper we give a numerically realizable explicit formula for solving the Cauchy problem in a two-dimensional domain for a general second-order linear elliptic equation with analytic coefficients and the Cauchy analytic data on the analytic boundary.

Publisher

IOP Publishing

Subject

General Physics and Astronomy

Reference14 articles.

1. Inverse problems in magneto-electroscanning (in encephalography, for magnetic microscopes, etc.);Demidov;Journal of Applied Analysis and Computation,2018

2. An inverse problem originating from magnethohydrodynamics;Beretta;Arch. Ration. Mech. Anal.,1991

3. An inverse problem originating from magnethohydrodynamics, II. The case of the Grad-Shafranov equation;Beretta;Indiana Univ. Math. J.,1992

4. An inverse problem originating from magnethohydrodynamics, III. Domains with corners of arbitrary angles;Beretta;Asympt. Anal.,1995

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