One‐dimensional flow of charged particles in a bounded system is investigated. In particular, the well‐known overlap of steady‐state solutions in the zero‐temperature flow approximation is examined in detail. A stability analysis is performed, and it is proved that not only the overlapping steady‐state solutions are unstable to infinitely small perturbations, but that all steady‐state flows in which partial reflection of charged particles from a virtual cathode is assumed, are also unstable.