On green’s function of second darboux problem for hyperbolic equation
A definition and justify a method for constructing the Green’s function of the second Darboux problem for a two-dimensional linear hyperbolic equation of the second order in a characteristic triangle is given. In contrast to the (well-developed) theory of the Green’s function for self-adjoint ellipt...
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| Format: | Article |
| Language: | English |
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Al-Farabi Kazakh National University
2022-12-01
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| Series: | Вестник КазНУ. Серия математика, механика, информатика |
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| Online Access: | https://bm.kaznu.kz/index.php/kaznu/article/view/1166/681 |
| _version_ | 1811173451690409984 |
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| author | B. Derbissaly |
| author_facet | B. Derbissaly |
| author_sort | B. Derbissaly |
| collection | DOAJ |
| description | A definition and justify a method for constructing the Green’s function of the second Darboux problem for a two-dimensional linear hyperbolic equation of the second order in a characteristic triangle is given. In contrast to the (well-developed) theory of the Green’s function for self-adjoint elliptic problems, this theory has not yet been developed. And for the case of asymmetric boundary value problems such studies have not been carried out. It is shown that the Green’s function for a hyperbolic equation of the general form can be constructed using the Riemann-Green function for some auxiliary hyperbolic equation. The notion of the Green’s function is more completely developed for Sturm-Liouville problems for an ordinary differential equation, for Dirichlet boundary value problems for Poisson equation, for initial boundary value problems for a heat equation. For many particular cases, the Greens’ function has been constructed explicitly. However, many more problems require their consideration. In this paper, the problem of constructing the Green’s function of the second Darboux problem for a hyperbolic equation was investigated. The Green’s function for the hyperbolic problems differs significantly from the Green’s function of problems for equations of elliptic and parabolic types. |
| first_indexed | 2024-04-10T17:47:08Z |
| format | Article |
| id | doaj.art-06e3fcb29c6646aeadbf232b7bd16da5 |
| institution | Directory Open Access Journal |
| issn | 1563-0277 2617-4871 |
| language | English |
| last_indexed | 2024-04-10T17:47:08Z |
| publishDate | 2022-12-01 |
| publisher | Al-Farabi Kazakh National University |
| record_format | Article |
| series | Вестник КазНУ. Серия математика, механика, информатика |
| spelling | doaj.art-06e3fcb29c6646aeadbf232b7bd16da52023-02-03T04:45:05ZengAl-Farabi Kazakh National UniversityВестник КазНУ. Серия математика, механика, информатика1563-02772617-48712022-12-011164314https://doi.org/10.26577/JMMCS.2022.v116.i4.01On green’s function of second darboux problem for hyperbolic equationB. Derbissaly0https://orcid.org/0000-0001-7976-4027Institute of Mathematics and Mathematical Modeling, Kazakhstan, AlmatyA definition and justify a method for constructing the Green’s function of the second Darboux problem for a two-dimensional linear hyperbolic equation of the second order in a characteristic triangle is given. In contrast to the (well-developed) theory of the Green’s function for self-adjoint elliptic problems, this theory has not yet been developed. And for the case of asymmetric boundary value problems such studies have not been carried out. It is shown that the Green’s function for a hyperbolic equation of the general form can be constructed using the Riemann-Green function for some auxiliary hyperbolic equation. The notion of the Green’s function is more completely developed for Sturm-Liouville problems for an ordinary differential equation, for Dirichlet boundary value problems for Poisson equation, for initial boundary value problems for a heat equation. For many particular cases, the Greens’ function has been constructed explicitly. However, many more problems require their consideration. In this paper, the problem of constructing the Green’s function of the second Darboux problem for a hyperbolic equation was investigated. The Green’s function for the hyperbolic problems differs significantly from the Green’s function of problems for equations of elliptic and parabolic types.https://bm.kaznu.kz/index.php/kaznu/article/view/1166/681hyperbolic equationnitial-boundary value problemsecond darboux problemboundary conditiongreen functiona characteristic triangleriemann–green function |
| spellingShingle | B. Derbissaly On green’s function of second darboux problem for hyperbolic equation Вестник КазНУ. Серия математика, механика, информатика hyperbolic equation nitial-boundary value problem second darboux problem boundary condition green function a characteristic triangle riemann–green function |
| title | On green’s function of second darboux problem for hyperbolic equation |
| title_full | On green’s function of second darboux problem for hyperbolic equation |
| title_fullStr | On green’s function of second darboux problem for hyperbolic equation |
| title_full_unstemmed | On green’s function of second darboux problem for hyperbolic equation |
| title_short | On green’s function of second darboux problem for hyperbolic equation |
| title_sort | on green s function of second darboux problem for hyperbolic equation |
| topic | hyperbolic equation nitial-boundary value problem second darboux problem boundary condition green function a characteristic triangle riemann–green function |
| url | https://bm.kaznu.kz/index.php/kaznu/article/view/1166/681 |
| work_keys_str_mv | AT bderbissaly ongreensfunctionofseconddarbouxproblemforhyperbolicequation |