On the expansion of a wedge of van der Waals gas into a vacuum II

We study the expansion of a wedge of rest gas into a vacuum. When the rest gas is a van der Waals gas, the gas away from the sharp corner of the wedge may expand into the vacuum as symmetrical planar rarefaction waves, planar fan-jump composite waves, or planar fan-jump-fan composite waves. So, in order to solve the expansion problem we need to study the interactions of these elementary waves. In a recent paper [17], we obtained the existence of global in time classical solution to the interaction of the planar rarefaction waves. This paper studies the interaction of the planar fan-jump composite waves. To construct the flow in the interaction region of the fan-jump composite waves, we consider a discontinuous Goursat problem for the two-dimensional self-similar Euler system. The existence of global solution to the discontinuous Goursat problem is obtained constructively by using the characteristic method.