The tri-harmonic Neumann problem
In this article investigated the tri-harmonic Neumann function for the unit dics. For harmonics functions the Neumann’s boundary problem is well studied and solved under certain conditions through Neumann’s function, sometimes it is also called Green’s function of the second order. Any case of find...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2018-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/236 |
| _version_ | 1797372688450191360 |
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| author | S. Burgumbayeva |
| author_facet | S. Burgumbayeva |
| author_sort | S. Burgumbayeva |
| collection | DOAJ |
| description |
In this article investigated the tri-harmonic Neumann function for the unit dics. For harmonics functions the Neumann’s boundary problem is well studied and solved under certain conditions through Neumann’s function, sometimes it is also called Green’s function of the second order. Any case of finding of Green function of the corresponding boundary value problem is very important for this or that area D as it contains extensive information, allowing to write out a large number of analytical solutions in the form of integrated ratios. At the same time the specified procedure makes the main difficulty at the solution Dirichlet and Neumann problems and in an explicit form Green function is known only for a small number of simple areas. The harmonics Green function with itself consistently leads to the subsequent polyharmonic Green function which can be used to solve the subsequent Dirichlet problem for higher order of the Poisson equation. Methods of integrated transformation have received tri-harmonic Neumann function in explicit form for the unit disc of the complex plane with biharmonic Neumann function. With Neumann’s function an integrated idea is given by development for the tri-harmonic operator. Above-mentioned polyharmonic Green function for the unit disc gives rise to the solution some specific polyharmonic objective of Dirichlet problem. In the same way harmonic Neumann function with itself consistently leads to the subsequent polyharmonic Neumann function. Received in the present article result allows to expect interesting prospects in further development of the analytical theory of boundary valua problems in complex analysis for the equations of elliptic type.
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| first_indexed | 2024-03-08T18:38:28Z |
| format | Article |
| id | doaj.art-ec33256dfdfd4c4098464f5ddc5bf3bd |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:28Z |
| publishDate | 2018-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-ec33256dfdfd4c4098464f5ddc5bf3bd2023-12-29T10:21:08ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112018-12-0192410.31489/2018m4/29-37The tri-harmonic Neumann problemS. Burgumbayeva In this article investigated the tri-harmonic Neumann function for the unit dics. For harmonics functions the Neumann’s boundary problem is well studied and solved under certain conditions through Neumann’s function, sometimes it is also called Green’s function of the second order. Any case of finding of Green function of the corresponding boundary value problem is very important for this or that area D as it contains extensive information, allowing to write out a large number of analytical solutions in the form of integrated ratios. At the same time the specified procedure makes the main difficulty at the solution Dirichlet and Neumann problems and in an explicit form Green function is known only for a small number of simple areas. The harmonics Green function with itself consistently leads to the subsequent polyharmonic Green function which can be used to solve the subsequent Dirichlet problem for higher order of the Poisson equation. Methods of integrated transformation have received tri-harmonic Neumann function in explicit form for the unit disc of the complex plane with biharmonic Neumann function. With Neumann’s function an integrated idea is given by development for the tri-harmonic operator. Above-mentioned polyharmonic Green function for the unit disc gives rise to the solution some specific polyharmonic objective of Dirichlet problem. In the same way harmonic Neumann function with itself consistently leads to the subsequent polyharmonic Neumann function. Received in the present article result allows to expect interesting prospects in further development of the analytical theory of boundary valua problems in complex analysis for the equations of elliptic type. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/236Neumann functionGreen functionharmonic functionpotentialfieldthe Dirichlet problem |
| spellingShingle | S. Burgumbayeva The tri-harmonic Neumann problem Қарағанды университетінің хабаршысы. Математика сериясы Neumann function Green function harmonic function potential field the Dirichlet problem |
| title | The tri-harmonic Neumann problem |
| title_full | The tri-harmonic Neumann problem |
| title_fullStr | The tri-harmonic Neumann problem |
| title_full_unstemmed | The tri-harmonic Neumann problem |
| title_short | The tri-harmonic Neumann problem |
| title_sort | tri harmonic neumann problem |
| topic | Neumann function Green function harmonic function potential field the Dirichlet problem |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/236 |
| work_keys_str_mv | AT sburgumbayeva thetriharmonicneumannproblem AT sburgumbayeva triharmonicneumannproblem |