On the unique solvability of a nonlocal boundary value problem with the poincaré condition
As is known, it is customary in the literature to divide degenerate equations of mixed type into equations of the first and second kind. In the case of an equation of the second kind, in contrast to the first, the degeneracy line is simultaneously the envelope of a family of characteristics, i.e. is...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2023-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/38/e3sconf_conmechydro23_03048.pdf |
| _version_ | 1797775913765568512 |
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| author | Abdullaev A. A. Safarbayeva N. M. Usmonov B. Z. |
| author_facet | Abdullaev A. A. Safarbayeva N. M. Usmonov B. Z. |
| author_sort | Abdullaev A. A. |
| collection | DOAJ |
| description | As is known, it is customary in the literature to divide degenerate equations of mixed type into equations of the first and second kind. In the case of an equation of the second kind, in contrast to the first, the degeneracy line is simultaneously the envelope of a family of characteristics, i.e. is itself a characteristic, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In this paper, in order to establish the unique solvability of one nonlocal problem with the Poincaré condition for an elliptic-hyperbolic equation of the second kind developed a new principle extremum, which helps to prove the uniqueness of resolutions as signed problem. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which known by the Carleman-Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem. |
| first_indexed | 2024-03-12T22:42:28Z |
| format | Article |
| id | doaj.art-a5b3092b71be49c8aa154b794ec773eb |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-03-12T22:42:28Z |
| publishDate | 2023-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-a5b3092b71be49c8aa154b794ec773eb2023-07-21T09:34:23ZengEDP SciencesE3S Web of Conferences2267-12422023-01-014010304810.1051/e3sconf/202340103048e3sconf_conmechydro23_03048On the unique solvability of a nonlocal boundary value problem with the poincaré conditionAbdullaev A. A.0Safarbayeva N. M.1Usmonov B. Z.2“Tashkent Institute of Irrigation and Agricultural Mechanization Engineers” National Research University“Tashkent Institute of Irrigation and Agricultural Mechanization Engineers” National Research UniversityChirchik State Pedagogical InstituteAs is known, it is customary in the literature to divide degenerate equations of mixed type into equations of the first and second kind. In the case of an equation of the second kind, in contrast to the first, the degeneracy line is simultaneously the envelope of a family of characteristics, i.e. is itself a characteristic, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In this paper, in order to establish the unique solvability of one nonlocal problem with the Poincaré condition for an elliptic-hyperbolic equation of the second kind developed a new principle extremum, which helps to prove the uniqueness of resolutions as signed problem. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which known by the Carleman-Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem.https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/38/e3sconf_conmechydro23_03048.pdf |
| spellingShingle | Abdullaev A. A. Safarbayeva N. M. Usmonov B. Z. On the unique solvability of a nonlocal boundary value problem with the poincaré condition E3S Web of Conferences |
| title | On the unique solvability of a nonlocal boundary value problem with the poincaré condition |
| title_full | On the unique solvability of a nonlocal boundary value problem with the poincaré condition |
| title_fullStr | On the unique solvability of a nonlocal boundary value problem with the poincaré condition |
| title_full_unstemmed | On the unique solvability of a nonlocal boundary value problem with the poincaré condition |
| title_short | On the unique solvability of a nonlocal boundary value problem with the poincaré condition |
| title_sort | on the unique solvability of a nonlocal boundary value problem with the poincare condition |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/38/e3sconf_conmechydro23_03048.pdf |
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