On an Approximate Solution of the Cauchy Problem for Systems of Equations of Elliptic Type of the First Order.
Entropy (Basel)
; 24(7)2022 Jul 13.
Article
em En
| MEDLINE
| ID: mdl-35885190
ABSTRACT
In this paper, on the basis of the Carleman matrix, we explicitly construct a regularized solution of the Cauchy problem for the matrix factorization of Helmholtz's equation in an unbounded two-dimensional domain. The focus of this paper is on regularization formulas for solutions to the Cauchy problem. The question of the existence of a solution to the problem is not considered-it is assumed a priori. At the same time, it should be noted that any regularization formula leads to an approximate solution of the Cauchy problem for all data, even if there is no solution in the usual classical sense. Moreover, for explicit regularization formulas, one can indicate in what sense the approximate solution turns out to be optimal.
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Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Entropy (Basel)
Ano de publicação:
2022
Tipo de documento:
Article
País de afiliação:
Uzbequistão