dc.contributor.author |
Alimov M. |
|
dc.date.accessioned |
2018-09-18T20:34:31Z |
|
dc.date.available |
2018-09-18T20:34:31Z |
|
dc.date.issued |
2011 |
|
dc.identifier.issn |
1995-0802 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/141291 |
|
dc.description.abstract |
A modification of Howison's method is proposed to construct exact nonstationary solutions of the unsteady two-phase Hele-Shaw problem (Muskat problem). The effectiveness of the modified method is demonstrated by reproducing D. Crowdy's exact solution for the evolution of an elliptic bubble of a viscous fluid surrounded by another fluid in an unbounded Hele-Shaw cell. This solution is found to be directly related to the explicit solution of the single-phase Hele-Shaw problem. A comparison of these solutions shows that allowance for the second phase leads to a weak regularizing effect: the single-phase solution exists over a finite time, while the two-phase solution exists over an infinite time under the same initial conditions. © 2011 Pleiades Publishing, Ltd. |
|
dc.relation.ispartofseries |
Lobachevskii Journal of Mathematics |
|
dc.subject |
elliptic bubble |
|
dc.subject |
Muskat problem |
|
dc.subject |
unsteady two-phase Hele-Shaw problem |
|
dc.title |
Construction of exact solutions to the Muskat problem |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
4 |
|
dc.relation.ispartofseries-volume |
32 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
404 |
|
dc.source.id |
SCOPUS19950802-2011-32-4-SID84862903637 |
|