Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order
We study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-stru...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/7/358 |
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| author | Davron Aslonqulovich Juraev Ali Shokri Daniela Marian |
| author_facet | Davron Aslonqulovich Juraev Ali Shokri Daniela Marian |
| author_sort | Davron Aslonqulovich Juraev |
| collection | DOAJ |
| description | We study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>m</mi></msup></semantics></math></inline-formula>. Based on the constructed Carleman matrix, we find an explicit form of the approximate solution of this problem and prove the stability of the solutions. |
| first_indexed | 2024-03-09T03:24:21Z |
| format | Article |
| id | doaj.art-50254a30a3db41c98ac75eece261e98f |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T03:24:21Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-50254a30a3db41c98ac75eece261e98f2023-12-03T15:04:42ZengMDPI AGFractal and Fractional2504-31102022-06-016735810.3390/fractalfract6070358Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First OrderDavron Aslonqulovich Juraev0Ali Shokri1Daniela Marian2Chair of Natural Science Disciplines, Higher Military Aviation School of the Republic of Uzbekistan, Karshi 180100, UzbekistanDepartment of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh 83111-55181, IranDepartment of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, RomaniaWe study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>m</mi></msup></semantics></math></inline-formula>. Based on the constructed Carleman matrix, we find an explicit form of the approximate solution of this problem and prove the stability of the solutions.https://www.mdpi.com/2504-3110/6/7/358Carleman matrixstability of the Cauchy problemregularized solutionapproximate solution |
| spellingShingle | Davron Aslonqulovich Juraev Ali Shokri Daniela Marian Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order Fractal and Fractional Carleman matrix stability of the Cauchy problem regularized solution approximate solution |
| title | Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order |
| title_full | Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order |
| title_fullStr | Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order |
| title_full_unstemmed | Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order |
| title_short | Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order |
| title_sort | solution of the ill posed cauchy problem for systems of elliptic type of the first order |
| topic | Carleman matrix stability of the Cauchy problem regularized solution approximate solution |
| url | https://www.mdpi.com/2504-3110/6/7/358 |
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