A class of discontinuous dynamical systems I. An ideal gas-liquid system

When a liquid and a gas are sent into a closed system and withdrawn through a single outlet, discontinuous behaviour results. Two different models are applicable to this system depending on whether the liquid or the gas flows out. The system switches between the gas flow and the liquid flow incessantly, reaching a state of sliding motion (Filippov, Differential Equations with Discontinuous Righthand Sides. Mathematics and its Applications (Soviet Series), Kluwer, Dordrecht, 1988). It is shown that the state of sliding motion is reached from all starting positions. The sliding motion is also shown to be stable. The steady state of the sliding motion can also be considered as a time-averaged steady state. Simulation results support these predictions. Similar results are obtained in the presence of a control valve. (C) 2001 .