On the scattering problem and problem of recovery of the shape of a graph
UDC 517.9 We consider a scattering problem generated by the Sturm–Liouville equation on a tree formed by an equilateral compact subtree with a lead (a half-infinite edge) attached to this compact subtree.  It is assumed that the potential on the lead by is identically equal to zero and...
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| Date: | 2024 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8151 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512940390612992 |
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| author | Boyko, O. Martynyuk, O. Pivovarchik, V. Бойко, Ольга Мартинюк, Ольга Пивоварчик, Вячеслав |
| author_facet | Boyko, O. Martynyuk, O. Pivovarchik, V. Бойко, Ольга Мартинюк, Ольга Пивоварчик, Вячеслав |
| author_sort | Boyko, O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-09-25T06:57:37Z |
| description | UDC 517.9
We consider a scattering problem generated by the Sturm–Liouville equation on a tree formed by an equilateral compact subtree with a lead (a half-infinite edge) attached to this compact subtree.  It is assumed that the potential on the lead by is identically equal to zero and the potentials on finite edges are real $L_2$-functions.  We show how to determine the shape of the tree by using the S-function and the eigenvalues of the scattering problem.  |
| doi_str_mv | 10.3842/umzh.v76i8.8151 |
| first_indexed | 2026-03-24T03:36:46Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8151 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:36:46Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9f/7c1a7bd55b8a1c638c808bfea7f6f69f |
| spelling | umjimathkievua-article-81512024-09-25T06:57:37Z On the scattering problem and problem of recovery of the shape of a graph Про задачу розсіяння та задачу відновлення форми графа Boyko, O. Martynyuk, O. Pivovarchik, V. Бойко, Ольга Мартинюк, Ольга Пивоварчик, Вячеслав Sturm-Liouville equation, eigenvalue, equilateral tree, star graph, Dirichlet boundary condition, Neumann boundary condition, lead, S-function, asymptotics. Рівняння Штурма-Ліувіля, власне значення, рівнобічне дерево, зірковий граф, крайова умова Діріхле, крайова умова Неймана, півнескінченне ребро, S-функція, асимптотика. UDC 517.9 We consider a scattering problem generated by the Sturm–Liouville equation on a tree formed by an equilateral compact subtree with a lead (a half-infinite edge) attached to this compact subtree.  It is assumed that the potential on the lead by is identically equal to zero and the potentials on finite edges are real $L_2$-functions.  We show how to determine the shape of the tree by using the S-function and the eigenvalues of the scattering problem.  УДК 517.9 Розглянуто задачу розсіяння Штурма–Ліувілля, породжену рівнянням Штурма–Ліувілля на дереві, яке складається з рівнобічного компактного піддерева з  жилою (напівнескінченним ребром), приєднаною до цього компактного підграфа. При цьому припускається, що потенціал на жилі тотожно нульовий, а потенціали на скінченних ребрах – дійсні функції з $L_2$. Показано як знайти форму дерева, використовуючи S-функцію та власні значення задачі розсіяння.  Institute of Mathematics, NAS of Ukraine 2024-09-04 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8151 10.3842/umzh.v76i8.8151 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 8 (2024); 1120 - 1131 Український математичний журнал; Том 76 № 8 (2024); 1120 - 1131 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/8151/10149 Copyright (c) 2024 Вячеслав Миколайович Пивоварчик |
| spellingShingle | Boyko, O. Martynyuk, O. Pivovarchik, V. Бойко, Ольга Мартинюк, Ольга Пивоварчик, Вячеслав On the scattering problem and problem of recovery of the shape of a graph |
| title | On the scattering problem and problem of recovery of the shape of a graph |
| title_alt | Про задачу розсіяння та задачу відновлення форми графа |
| title_full | On the scattering problem and problem of recovery of the shape of a graph |
| title_fullStr | On the scattering problem and problem of recovery of the shape of a graph |
| title_full_unstemmed | On the scattering problem and problem of recovery of the shape of a graph |
| title_short | On the scattering problem and problem of recovery of the shape of a graph |
| title_sort | on the scattering problem and problem of recovery of the shape of a graph |
| topic_facet | Sturm-Liouville equation eigenvalue equilateral tree star graph Dirichlet boundary condition Neumann boundary condition lead S-function asymptotics. Рівняння Штурма-Ліувіля власне значення рівнобічне дерево зірковий граф крайова умова Діріхле крайова умова Неймана півнескінченне ребро S-функція асимптотика. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8151 |
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