Abstract
A Hele-Shaw problem with a time-dependent width of the gap i s considered. A governing equation in terms of the Schwarz function of the free boundary for a class of generalized Hele-Shaw flows, which includes the problem with a time-dependent gap as a special case, is derived. The exact solution is obtained for the droplet with initial elliptical shape when the surface tension is neglected, and the asymptotic solution is obtained when the surface tension is taken into account.