The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension
In the paper, we consider the two-dimensional Muskat problem without surface tension on a free boundary. The initial shape of the unknown interface has a corner point. We prove that the problem has a unique solution in the weighted Hölder classes locally in time and specify the sufficient conditions...
Збережено в:
| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2014
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106784 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension / B.V. Bazaliy, N. Vasylyeva // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 1. — С. 3-43. — Бібліогр.: 31 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106784 |
|---|---|
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dspace |
| spelling |
irk-123456789-1067842017-05-27T16:10:57Z The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension Bazaliy, B.V. Vasylyeva, N. In the paper, we consider the two-dimensional Muskat problem without surface tension on a free boundary. The initial shape of the unknown interface has a corner point. We prove that the problem has a unique solution in the weighted Hölder classes locally in time and specify the sufficient conditions for the existence of the "waiting time" phenomenon. Изучается задача Маскета без учета поверхностного натяжения свободной границы. Неизвестная граница в начальный момент времени имеет угловую точку. Доказывается существование и единственность локального решения в весовых пространствах Гельдера, находятся достаточные условия на начальные данные, при которых существует феномен "времени ожидания". 2014 Article The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension / B.V. Bazaliy, N. Vasylyeva // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 1. — С. 3-43. — Бібліогр.: 31 назв. — англ. 1812-9471 DOI: 10.15407/mag10.01.003 MSC2000: 35R35 (primary); 35J25, 35B65 (secondary). http://dspace.nbuv.gov.ua/handle/123456789/106784 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In the paper, we consider the two-dimensional Muskat problem without surface tension on a free boundary. The initial shape of the unknown interface has a corner point. We prove that the problem has a unique solution in the weighted Hölder classes locally in time and specify the sufficient conditions for the existence of the "waiting time" phenomenon. |
| format |
Article |
| author |
Bazaliy, B.V. Vasylyeva, N. |
| spellingShingle |
Bazaliy, B.V. Vasylyeva, N. The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension Журнал математической физики, анализа, геометрии |
| author_facet |
Bazaliy, B.V. Vasylyeva, N. |
| author_sort |
Bazaliy, B.V. |
| title |
The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension |
| title_short |
The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension |
| title_full |
The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension |
| title_fullStr |
The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension |
| title_full_unstemmed |
The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension |
| title_sort |
two-phase hele-shaw problem with a nonregular initial interface and without surface tension |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106784 |
| citation_txt |
The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension / B.V. Bazaliy, N. Vasylyeva // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 1. — С. 3-43. — Бібліогр.: 31 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
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| first_indexed |
2023-10-18T20:13:41Z |
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2023-10-18T20:13:41Z |
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1796149308462989312 |