Free and moving boundary problems in hydrodynamics.

Discusses well posed and ill posed problems in free surface flows in porous media (with or without gravity) and the two dimensional Hele Shaw cell analogue. Examines models for these flows, related heat and mass transfer problems, and studies local stability analyses. Establishes well posedness criteria. Discusses the rectangular dam problem and considers exact and approximate methods of solution. Develops an asymptotic approximation for cases where change in fluid level is small compared to overall dam dimensions. Derives explicit solutions from a linear formulation, and also treats the problem as a variational inequality. Studies Hele Shaw flow without gravity and presents a class of explicit solutions for unsteady flow. These solutions break down in finite time. Examines surface tension effects and proposes a numerical method for ill posed Hele Shaw flow. Presents numerical results. (C.J.U.)