Convex dynamics in Hele-Shaw cells
We study geometric properties of a contracting bubble driven by a homogeneous source at infinity and surface tension. The properties that are preserved during the time evolution are under consideration. In particular, we study convex dynamics of the bubble and prove that the rate of the area change...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202203142 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552016824500224 |
|---|---|
| author | Dmitri Prokhorov Alexander Vasil'ev |
| author_facet | Dmitri Prokhorov Alexander Vasil'ev |
| author_sort | Dmitri Prokhorov |
| collection | DOAJ |
| description | We study geometric properties of a contracting bubble
driven by a homogeneous source at infinity and surface tension.
The properties that are preserved during the time evolution are
under consideration. In particular, we study convex dynamics of
the bubble and prove that the rate of the area change is
controlled by variation of the bubble logarithmic capacity. Next
we consider injection through a single finite source and study
some isoperimetric inequalities that correspond to the convex and
α-convex dynamics. |
| format | Article |
| id | doaj-art-68e844463c0e44a6a72554cb07c8b121 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-68e844463c0e44a6a72554cb07c8b1212025-02-03T05:59:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01311163965010.1155/S0161171202203142Convex dynamics in Hele-Shaw cellsDmitri Prokhorov0Alexander Vasil'ev1Department of Mathematics and Mechanics, Saratov State University, Saratov 410026, RussiaDepartamento de Matemática, UTFSM, Casilla, Valparaíso 110-V, ChileWe study geometric properties of a contracting bubble driven by a homogeneous source at infinity and surface tension. The properties that are preserved during the time evolution are under consideration. In particular, we study convex dynamics of the bubble and prove that the rate of the area change is controlled by variation of the bubble logarithmic capacity. Next we consider injection through a single finite source and study some isoperimetric inequalities that correspond to the convex and α-convex dynamics.http://dx.doi.org/10.1155/S0161171202203142 |
| spellingShingle | Dmitri Prokhorov Alexander Vasil'ev Convex dynamics in Hele-Shaw cells International Journal of Mathematics and Mathematical Sciences |
| title | Convex dynamics in Hele-Shaw cells |
| title_full | Convex dynamics in Hele-Shaw cells |
| title_fullStr | Convex dynamics in Hele-Shaw cells |
| title_full_unstemmed | Convex dynamics in Hele-Shaw cells |
| title_short | Convex dynamics in Hele-Shaw cells |
| title_sort | convex dynamics in hele shaw cells |
| url | http://dx.doi.org/10.1155/S0161171202203142 |
| work_keys_str_mv | AT dmitriprokhorov convexdynamicsinheleshawcells AT alexandervasilev convexdynamicsinheleshawcells |