On the Approximate Solution of the Cauchy Problem in a Multidimensional Unbounded Domain-Reference-Cited by-同舟云学术

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On the Approximate Solution of the Cauchy Problem in a Multidimensional Unbounded Domain

Published:2022-07-21 Issue:7 Volume:6 Page:403
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Juraev Davron Aslonqulovich^ORCID,Shokri Ali^ORCID,Marian Daniela^ORCID

Abstract

In this paper, the Carleman matrix is constructed, and based on it we found explicitly a regularized solution of the Cauchy problem for the matrix factorization of the Helmholtz equation in a multidimensional unbounded domain in Rm,(m=2k,k≥2). The corresponding theorems on the stability of the solution of problems are proved.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/6/7/403/pdf

Reference35 articles.

1. The Cauchy Problem for Linear Partial Differential Equations of Hyperbolic Type;Hadamard,1978

2. On the solution of ill-posed problems and the method of regularization;Tikhonov;Dokl. Akad. Nauk. SSSR,1963

3. Les Fonctions Quasi Analytiques;Carleman,1926

4. The generalized Carleman formula and its application to the analytic continuation of functions;Goluzin;Sb. Math.,1933

5. On the Cauchy problem for second-order linear elliptic equations;Lavrent’ev;Rep. USSR Acad. Sci.,1957

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