A parabolic equation for the fractional Laplacian in the whole space: blow-up of nonnegative solutions
UDC 517.9 The main aim of the present paper is to investigate under what conditions the nonnegative solutions blow-up for the parabolic problem $\dfrac{\partial u}{\partial t} = - (-\triangle)^{\frac{\alpha}{2}}u + \dfrac{c}{|x|^{\alpha}}u$ in $\mathbb{R}^{d}\times (0 , T),$ where $0
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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1531 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860507326164762624 |
|---|---|
| author | Kenzizi, T. Кензізі, Т. |
| author_facet | Kenzizi, T. Кензізі, Т. |
| author_sort | Kenzizi, T. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-02-09T14:27:57Z |
| description | UDC 517.9
The main aim of the present paper is to investigate under what conditions the nonnegative solutions blow-up for the parabolic problem
$\dfrac{\partial u}{\partial t} = - (-\triangle)^{\frac{\alpha}{2}}u + \dfrac{c}{|x|^{\alpha}}u$ in $\mathbb{R}^{d}\times (0 , T),$ where $0 |
| doi_str_mv | 10.3842/umzh.v71i11.1531 |
| first_indexed | 2026-03-24T02:07:32Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-1531 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:07:32Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/2c/1bac47a1bf66a6eed5e6c724eb3a362c |
| spelling | umjimathkievua-article-15312026-02-09T14:27:57Z A parabolic equation for the fractional Laplacian in the whole space: blow-up of nonnegative solutions Параболiчне рiвняння для дробового лапласiана в усьому просторi: вибух невiд’ємних розв’язкiв Kenzizi, T. Кензізі, Т. UDC 517.9 The main aim of the present paper is to investigate under what conditions the nonnegative solutions blow-up for the parabolic problem $\dfrac{\partial u}{\partial t} = - (-\triangle)^{\frac{\alpha}{2}}u + \dfrac{c}{|x|^{\alpha}}u$ in $\mathbb{R}^{d}\times (0 , T),$ where $0 УДК 517.9 Вивчено умови, за яких ,,вибухають'' невід’ємні розв'язки параболічної задачі $\dfrac{\partial u}{\partial t} = - (-\triangle)^{\frac{\alpha}{2}}u + \dfrac{c}{|x|^{\alpha}}u$ в $\mathbb{R}^{d} \times (0 , T),$ де $0 Institute of Mathematics, NAS of Ukraine 2026-02-09 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/1531 10.3842/umzh.v71i11.1531 Ukrains’kyi Matematychnyi Zhurnal; Vol. 71 No. 11 (2019); 1502-1518 Український математичний журнал; Том 71 № 11 (2019); 1502-1518 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/1531/513 Copyright (c) 2019 Kenzizi T. |
| spellingShingle | Kenzizi, T. Кензізі, Т. A parabolic equation for the fractional Laplacian in the whole space: blow-up of nonnegative solutions |
| title | A parabolic equation for the fractional Laplacian in the whole space: blow-up
of nonnegative solutions |
| title_alt | Параболiчне рiвняння для дробового лапласiана
в усьому просторi: вибух невiд’ємних розв’язкiв |
| title_full | A parabolic equation for the fractional Laplacian in the whole space: blow-up
of nonnegative solutions |
| title_fullStr | A parabolic equation for the fractional Laplacian in the whole space: blow-up
of nonnegative solutions |
| title_full_unstemmed | A parabolic equation for the fractional Laplacian in the whole space: blow-up
of nonnegative solutions |
| title_short | A parabolic equation for the fractional Laplacian in the whole space: blow-up
of nonnegative solutions |
| title_sort | parabolic equation for the fractional laplacian in the whole space: blow-up
of nonnegative solutions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/1531 |
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