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On the Cauchy Problem 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.