The present paper concerns the study of a Riemann problem for the system , with a one dimensional space variable. We consider φ an entire function that takes real values on the real axis. Under certain conditions, this system provides solutions to the pressureless gas dynamics and the isentropic fluid dynamics systems. We get all solutions of this problem within a convenient space of distributions that contains discontinuous functions and Dirac measures. For this purpose, we use a solution concept defined in the setting of a distributional product. This concept consistently extends the classical solution concept and can also be considered as an extension of the weak solution concept for nonlinear evolution equations. Our product, not defined by approximation processes, can be applied to several physical models.