International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 11, Pages 639-650
Convex dynamics in Hele-Shaw cells
1Department of Mathematics and Mechanics, Saratov State University, Saratov 410026, Russia
2Departamento de Matemática, UTFSM, Casilla, Valparaíso 110-V, Chile
Received 15 March 2002
Copyright © 2002 Dmitri Prokhorov and Alexander Vasil'ev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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