Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kind
Equations of mixed type, the degeneracy line of which is the envelope of a family of characteristics, therefore, is itself also a characteristic, in the literature it is customary to call equations of mixed type of the second kind, which causes additional difficulties in the study of boundary value...
| Main Authors: | , , |
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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_03049.pdf |
| _version_ | 1797775925700460544 |
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| author | Abdullaev A. A. Xolbekov J. A. Axralov H. |
| author_facet | Abdullaev A. A. Xolbekov J. A. Axralov H. |
| author_sort | Abdullaev A. A. |
| collection | DOAJ |
| description | Equations of mixed type, the degeneracy line of which is the envelope of a family of characteristics, therefore, is itself also a characteristic, in the literature it is customary to call equations of mixed type of the second kind, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In the present work, a boundary value problem for a homogeneous equation of parabolic-hyperbolic type of the third order of the second kind is investigated. Necessary and sufficient conditions for the existence and uniqueness of a generalized solution of the problem are found. In some special cases, the representation of the solution of the problem under study is written out explicitly. |
| first_indexed | 2024-03-12T22:42:40Z |
| format | Article |
| id | doaj.art-d155ae64a592445580e9cd5de8a8730c |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-03-12T22:42:40Z |
| publishDate | 2023-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-d155ae64a592445580e9cd5de8a8730c2023-07-21T09:34:23ZengEDP SciencesE3S Web of Conferences2267-12422023-01-014010304910.1051/e3sconf/202340103049e3sconf_conmechydro23_03049Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kindAbdullaev A. A.0Xolbekov J. A.1Axralov H.2“Tashkent Institute of Irrigation and Agricultural Mechanization Engineers” National Research UniversityTashkent State Technical UniversityTashkent State Technical UniversityEquations of mixed type, the degeneracy line of which is the envelope of a family of characteristics, therefore, is itself also a characteristic, in the literature it is customary to call equations of mixed type of the second kind, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In the present work, a boundary value problem for a homogeneous equation of parabolic-hyperbolic type of the third order of the second kind is investigated. Necessary and sufficient conditions for the existence and uniqueness of a generalized solution of the problem are found. In some special cases, the representation of the solution of the problem under study is written out explicitly.https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/38/e3sconf_conmechydro23_03049.pdf |
| spellingShingle | Abdullaev A. A. Xolbekov J. A. Axralov H. Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kind E3S Web of Conferences |
| title | Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kind |
| title_full | Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kind |
| title_fullStr | Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kind |
| title_full_unstemmed | Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kind |
| title_short | Dirichlet’s problem for a third-order parabolic hyperbolic type equation of the second kind |
| title_sort | dirichlet s problem for a third order parabolic hyperbolic type equation of the second kind |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/38/e3sconf_conmechydro23_03049.pdf |
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