On the Cauchy Prolem for the p-System at a Junction

We present a model for the description of a nonviscous
isentropic or isothermal fluid crossing a junction. Aiming at an
extension of the usual Euler equations, we neglect the effects of
friction against the walls of the pipes, but the reaction
constraints at the junction are considered. The well posedness
of the Cauchy problem is proved, and some qualitative properties
of the model are described.