On the estimates of the rate of stabilization for some problems with free boundary
With the help of energy estimates we study the behavior of solutions of the Dirichlet problem and the Stefan problem under unbounded growth of time for the semilinear equation $u_t–u_{xx}+u^{\beta}=0$, $\beta \in (0,1)$, in the case of one geometric variable.
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| Date: | 1992 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8224 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512983017324544 |
|---|---|
| author | Bazaly, В. V. Tedeev, A. F. Базалий, Б. В. Тедеев, А . Ф. |
| author_facet | Bazaly, В. V. Tedeev, A. F. Базалий, Б. В. Тедеев, А . Ф. |
| author_sort | Bazaly, В. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-03-27T09:55:23Z |
| description | With the help of energy estimates we study the behavior of solutions of the Dirichlet problem and the Stefan problem under unbounded growth of time for the semilinear equation $u_t–u_{xx}+u^{\beta}=0$, $\beta \in (0,1)$, in the case of one geometric variable. |
| first_indexed | 2026-03-24T03:37:27Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8224 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:37:27Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f8/060d3815a22797b9eda403396b0e9bf8.pdf |
| spelling | umjimathkievua-article-82242024-03-27T09:55:23Z On the estimates of the rate of stabilization for some problems with free boundary Об оценках скорости стабилизации некоторых задач со свободной границей Bazaly, В. V. Tedeev, A. F. Базалий, Б. В. Тедеев, А . Ф. With the help of energy estimates we study the behavior of solutions of the Dirichlet problem and the Stefan problem under unbounded growth of time for the semilinear equation $u_t–u_{xx}+u^{\beta}=0$, $\beta \in (0,1)$, in the case of one geometric variable. С помощью энергетических оценок изучено поведение решений задачи Дирихле и задачи Стефана при неограниченном возрастании времени для полулинейного уравнения $u_t–u_{xx}+u^{\beta}=0$, $\beta \in (0,1)$ в случае одной геометрической переменной. За допомогою енергетичних оцінок вивчено поведінку розв’язків задачі Діріхле та задачі Стефана при нескінченному зростанні часу для напівлінійного рівняння $u_t–u_{xx}+u^{\beta}=0$, $\beta \in (0,1)$, у випадку однієї геометричної змінної. Institute of Mathematics, NAS of Ukraine 1992-10-01 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8224 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 10 (1992); 1299-1306 Український математичний журнал; Том 44 № 10 (1992); 1299-1306 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8224/9804 Copyright (c) 1992 В. V. Bazaly, A. F. Tedeev |
| spellingShingle | Bazaly, В. V. Tedeev, A. F. Базалий, Б. В. Тедеев, А . Ф. On the estimates of the rate of stabilization for some problems with free boundary |
| title | On the estimates of the rate of stabilization for some problems with free boundary |
| title_alt | Об оценках скорости стабилизации некоторых задач со свободной границей |
| title_full | On the estimates of the rate of stabilization for some problems with free boundary |
| title_fullStr | On the estimates of the rate of stabilization for some problems with free boundary |
| title_full_unstemmed | On the estimates of the rate of stabilization for some problems with free boundary |
| title_short | On the estimates of the rate of stabilization for some problems with free boundary |
| title_sort | on the estimates of the rate of stabilization for some problems with free boundary |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8224 |
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