On a boundary value problem for a parabolic-hyperbolic equation of the fourth order
In this paper a boundary value problem for a fourth-order equation of parabolic-hyperbolic type within a pentagonal domain was investigated. In the equation under consideration, one characteristic aligns with the Ox axis while the other aligns with the Oy axis. Initially, the problem was examined w...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2025-03-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/776 |
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| author | M. Mamajonov |
| author_facet | M. Mamajonov |
| author_sort | M. Mamajonov |
| collection | DOAJ |
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In this paper a boundary value problem for a fourth-order equation of parabolic-hyperbolic type within a pentagonal domain was investigated. In the equation under consideration, one characteristic aligns with the Ox axis while the other aligns with the Oy axis. Initially, the problem was examined within the lower triangle of the specified domain. Utilizing a differential equation solution construction method, a solution to the formulated problem was derived. Subsequently, within the rectangles of the domain, employing the continuation method, two relationships between the solution’s traces were established. Moreover, from the parabolic segment of the domain, two additional relationships between unknown traces will be derived. Solving this system of four equations enables determination of these traces, thereby resolving the problem.
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| format | Article |
| id | doaj-art-997d9033032a44f491efa10643519cd8 |
| institution | DOAJ |
| issn | 2518-7929 2663-5011 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj-art-997d9033032a44f491efa10643519cd82025-08-20T02:48:39ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112025-03-01117110.31489/2025m1/118-132On a boundary value problem for a parabolic-hyperbolic equation of the fourth orderM. Mamajonov0https://orcid.org/0009-0003-8413-0549Kokand State Pedagogical Institute, Kokand, Uzbekistan In this paper a boundary value problem for a fourth-order equation of parabolic-hyperbolic type within a pentagonal domain was investigated. In the equation under consideration, one characteristic aligns with the Ox axis while the other aligns with the Oy axis. Initially, the problem was examined within the lower triangle of the specified domain. Utilizing a differential equation solution construction method, a solution to the formulated problem was derived. Subsequently, within the rectangles of the domain, employing the continuation method, two relationships between the solution’s traces were established. Moreover, from the parabolic segment of the domain, two additional relationships between unknown traces will be derived. Solving this system of four equations enables determination of these traces, thereby resolving the problem. https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/776characteristic of the equationdifferential and integral equationsmethod of constructing a solutionboundary value problemequations of parabolic-hyperbolic typethe line of type changing |
| spellingShingle | M. Mamajonov On a boundary value problem for a parabolic-hyperbolic equation of the fourth order Қарағанды университетінің хабаршысы. Математика сериясы characteristic of the equation differential and integral equations method of constructing a solution boundary value problem equations of parabolic-hyperbolic type the line of type changing |
| title | On a boundary value problem for a parabolic-hyperbolic equation of the fourth order |
| title_full | On a boundary value problem for a parabolic-hyperbolic equation of the fourth order |
| title_fullStr | On a boundary value problem for a parabolic-hyperbolic equation of the fourth order |
| title_full_unstemmed | On a boundary value problem for a parabolic-hyperbolic equation of the fourth order |
| title_short | On a boundary value problem for a parabolic-hyperbolic equation of the fourth order |
| title_sort | on a boundary value problem for a parabolic hyperbolic equation of the fourth order |
| topic | characteristic of the equation differential and integral equations method of constructing a solution boundary value problem equations of parabolic-hyperbolic type the line of type changing |
| url | https://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/776 |
| work_keys_str_mv | AT mmamajonov onaboundaryvalueproblemforaparabolichyperbolicequationofthefourthorder |