On one proof of the classical solvability of the Hele-Shaw problem with free boundary
We consider the Stefan problem for a parabolic equation with a small parameter as the coefficient of the derivative with respect to time. We justify the limit transition as the small parameter tends to zero, which enables us to prove the classical solvability of the Hele-Shaw problem with free bound...
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| Date: | 1998 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4797 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510974875795456 |
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| author | Bazalii, B. V. Базалий, Б. В. Базалий, Б. В. |
| author_facet | Bazalii, B. V. Базалий, Б. В. Базалий, Б. В. |
| author_sort | Bazalii, B. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:14:51Z |
| description | We consider the Stefan problem for a parabolic equation with a small parameter as the coefficient of the derivative with respect to time. We justify the limit transition as the small parameter tends to zero, which enables us to prove the classical solvability of the Hele-Shaw problem with free boundary in the small with respect to time. |
| first_indexed | 2026-03-24T03:05:32Z |
| format | Article |
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| id | umjimathkievua-article-4797 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:05:32Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/33/c8e12e262c29c12583555718411fbb33.pdf |
| spelling | umjimathkievua-article-47972020-03-18T21:14:51Z On one proof of the classical solvability of the Hele-Shaw problem with free boundary Об одном доказательстве классической разрешимости задачи Hele - Shaw со свободной границей Bazalii, B. V. Базалий, Б. В. Базалий, Б. В. We consider the Stefan problem for a parabolic equation with a small parameter as the coefficient of the derivative with respect to time. We justify the limit transition as the small parameter tends to zero, which enables us to prove the classical solvability of the Hele-Shaw problem with free boundary in the small with respect to time. Розглянуто задачу Стефана для параболічного рівняння з малим параметром при похідній за часом. Наведено обгрунтування граничного переходу при наближенні малого параметру до нуля, що призводить до доказу класичної розв'язності задачі Hele - Shaw з вільною межею в малому за часом. Institute of Mathematics, NAS of Ukraine 1998-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4797 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 11 (1998); 1452–1462 Український математичний журнал; Том 50 № 11 (1998); 1452–1462 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4797/6293 https://umj.imath.kiev.ua/index.php/umj/article/view/4797/6294 Copyright (c) 1998 Bazalii B. V. |
| spellingShingle | Bazalii, B. V. Базалий, Б. В. Базалий, Б. В. On one proof of the classical solvability of the Hele-Shaw problem with free boundary |
| title | On one proof of the classical solvability of the Hele-Shaw problem with free boundary |
| title_alt | Об одном доказательстве классической разрешимости задачи Hele - Shaw со свободной границей |
| title_full | On one proof of the classical solvability of the Hele-Shaw problem with free boundary |
| title_fullStr | On one proof of the classical solvability of the Hele-Shaw problem with free boundary |
| title_full_unstemmed | On one proof of the classical solvability of the Hele-Shaw problem with free boundary |
| title_short | On one proof of the classical solvability of the Hele-Shaw problem with free boundary |
| title_sort | on one proof of the classical solvability of the hele-shaw problem with free boundary |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4797 |
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