On some boundary value problems for linear multidimensional hyperbolic equations of the second order
For the linear hyperbolic equations \[\sum_{i,j=1}^{m+1} a_{ij}(x,x_{m+1})u_{x_ix_j}+\sum_{i=1}^{m+1} a_i(x,x_{m+1})u_{x_i}+c(x,x_{m+1})u=0, \] \[x=(x_1,\dots,x_m), \, m\geq2\] the correctness of multidimensional analogues of the problems of Darboux and Goursat is established and a theorem on the un...
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| Datum: | 1991 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1991
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9624 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513544411283456 |
|---|---|
| author | Aldashev , S. A. Алдашев , С. А. |
| author_facet | Aldashev , S. A. Алдашев , С. А. |
| author_sort | Aldashev , S. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-10-09T12:05:28Z |
| description | For the linear hyperbolic equations
\[\sum_{i,j=1}^{m+1} a_{ij}(x,x_{m+1})u_{x_ix_j}+\sum_{i=1}^{m+1} a_i(x,x_{m+1})u_{x_i}+c(x,x_{m+1})u=0, \]
\[x=(x_1,\dots,x_m), \, m\geq2\]
the correctness of multidimensional analogues of the problems of Darboux and Goursat is established and a theorem on the uniqueness of a solution of the Cauchy characteristic problem is proved. |
| first_indexed | 2026-03-24T03:46:22Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-9624 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:46:22Z |
| publishDate | 1991 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/41/178bb39d67d6a50ea19fabaec1277e41 |
| spelling | umjimathkievua-article-96242025-10-09T12:05:28Z On some boundary value problems for linear multidimensional hyperbolic equations of the second order О некоторых краевых задачах для линейных многомерных гиперболических уравнений второго порядка Aldashev , S. A. Алдашев , С. А. - For the linear hyperbolic equations \[\sum_{i,j=1}^{m+1} a_{ij}(x,x_{m+1})u_{x_ix_j}+\sum_{i=1}^{m+1} a_i(x,x_{m+1})u_{x_i}+c(x,x_{m+1})u=0, \] \[x=(x_1,\dots,x_m), \, m\geq2\] the correctness of multidimensional analogues of the problems of Darboux and Goursat is established and a theorem on the uniqueness of a solution of the Cauchy characteristic problem is proved. Для линейных гиперболических уравнений \[\sum_{i,j=1}^{m+1} a_{ij}(x,x_{m+1})u_{x_ix_j}+\sum_{i=1}^{m+1} a_i(x,x_{m+1})u_{x_i}+c(x,x_{m+1})u=0,\] \[x=(x_1,\dots,x_m), \, m\geq2\] установлены корректности многомерных аналогов задач Дарбу и Гурса, а также доказана теорема единственности решения характеристической задачи Коши. Для лінійних гіперболічних рівнянь \[\sum_{i,j=1}^{m+1} a_{ij}(x,x_{m+1})u_{x_ix_j}+\sum_{i=1}^{m+1} a_i(x,x_{m+1})u_{x_i}+c(x,x_{m+1})u=0, \] \[x=(x_1,\dots,x_m), \, m\geq2\] досліджена коректність багатовимірних аналогів задач Дарбу і Гурса, а також доведена теорема єдності розв’язку характеристичної задачі Коші. Institute of Mathematics, NAS of Ukraine 1991-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9624 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 3 (1991); 415-420 Український математичний журнал; Том 43 № 3 (1991); 415-420 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9624/10592 Copyright (c) 1991 С. А. Алдашев |
| spellingShingle | Aldashev , S. A. Алдашев , С. А. On some boundary value problems for linear multidimensional hyperbolic equations of the second order |
| title | On some boundary value problems for linear multidimensional hyperbolic equations of the second order |
| title_alt | О некоторых краевых задачах для линейных многомерных гиперболических уравнений второго порядка |
| title_full | On some boundary value problems for linear multidimensional hyperbolic equations of the second order |
| title_fullStr | On some boundary value problems for linear multidimensional hyperbolic equations of the second order |
| title_full_unstemmed | On some boundary value problems for linear multidimensional hyperbolic equations of the second order |
| title_short | On some boundary value problems for linear multidimensional hyperbolic equations of the second order |
| title_sort | on some boundary value problems for linear multidimensional hyperbolic equations of the second order |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9624 |
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