Boundary-value problems for hyperbolic equations with constant coefficients
By using a metric approach, we study the problem of well-posedness of boundary-value problems for hyperbolic equations of ordern $(n ≥ 2)$ with constant coefficients in a cylindrical domain. Conditions of existence and uniqueness of solutions are formulated in number-theoretic terms. We prove a metr...
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| Date: | 1994 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5669 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511897356337152 |
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| author | Bobyk, I. O. Ptashnik, B. I. Бобик, І. О. Пташник, Б. Й. |
| author_facet | Bobyk, I. O. Ptashnik, B. I. Бобик, І. О. Пташник, Б. Й. |
| author_sort | Bobyk, I. O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:15:43Z |
| description | By using a metric approach, we study the problem of well-posedness of boundary-value problems for hyperbolic equations of ordern $(n ≥ 2)$ with constant coefficients in a cylindrical domain. Conditions of existence and uniqueness of solutions are formulated in number-theoretic terms. We prove a metric theorem on lower estimates of small denominators that appear when constructing solutions. |
| first_indexed | 2026-03-24T03:20:11Z |
| format | Article |
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| id | umjimathkievua-article-5669 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:20:11Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/1e/3513d1c531b82051846b73ad8ce4cf1e.pdf |
| spelling | umjimathkievua-article-56692020-03-19T09:15:43Z Boundary-value problems for hyperbolic equations with constant coefficients Крайові задачі для гіперболічних рівнянь зі сталими коефіцієнтами Bobyk, I. O. Ptashnik, B. I. Бобик, І. О. Пташник, Б. Й. By using a metric approach, we study the problem of well-posedness of boundary-value problems for hyperbolic equations of ordern $(n ≥ 2)$ with constant coefficients in a cylindrical domain. Conditions of existence and uniqueness of solutions are formulated in number-theoretic terms. We prove a metric theorem on lower estimates of small denominators that appear when constructing solutions. На основі метричного підходу досліджено питання коректності крайових задач для гіперболічних рівнянь $n$-го порядку $(n ≥ 2)$ зі сталими коефіцієнтами в циліндричній області. Умови існування та сяйності розв'язків задач формулюються в теоретико-числових термінах. Доведено метричну теорему про оцінки знизу малих знаменників, які виникають при побудові розв'язків задач. Institute of Mathematics, NAS of Ukraine 1994-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5669 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 7 (1994); 795–802 Український математичний журнал; Том 46 № 7 (1994); 795–802 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5669/8023 https://umj.imath.kiev.ua/index.php/umj/article/view/5669/8024 Copyright (c) 1994 Bobyk I. O.; Ptashnik B. I. |
| spellingShingle | Bobyk, I. O. Ptashnik, B. I. Бобик, І. О. Пташник, Б. Й. Boundary-value problems for hyperbolic equations with constant coefficients |
| title | Boundary-value problems for hyperbolic equations with constant coefficients |
| title_alt | Крайові задачі для гіперболічних рівнянь зі сталими коефіцієнтами |
| title_full | Boundary-value problems for hyperbolic equations with constant coefficients |
| title_fullStr | Boundary-value problems for hyperbolic equations with constant coefficients |
| title_full_unstemmed | Boundary-value problems for hyperbolic equations with constant coefficients |
| title_short | Boundary-value problems for hyperbolic equations with constant coefficients |
| title_sort | boundary-value problems for hyperbolic equations with constant coefficients |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5669 |
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