An exact solution to the one-phase zero-surface-tension Hele-Shaw free-boundary problem

A family of explicit solutions are presented to the one-phase zero-surface-tension Hele-Shaw problem with a single source/sink. The free boundary is described as a function of three parameters, whose dependence on time is evaluated through two different yet complementary methods. Possible mechanisms for nonexistence beyond a critical time are found in the case of both a contracting and expanding fluid region.