Delta wave and vacuum state for generalized Chaplygin gas dynamics system as pressure vanishes

This paper is concerned with the Riemann problems for the system of generalized Chaplygin gas dynamics and the formation of Delta wave and vacuum state as pressure vanishes. It is proved that, the limit solutions tend to the two kinds of Riemann solutions to the transport equations in zero-pressure flow, which include a Delta wave formed by a weighted δδ-measure and a vacuum state.