  We consider a quasilinear system of hyperbolic equations that describes plane
one-dimensional non-relativistic oscillations of electrons in a cold plasma
with allowance for electron-ion collisions. Accounting for collisions leads to
the appearance of a term analogous to dry friction in a mechanical system,
leading to a decrease in the total energy. We obtain a criterion for the
existence of a global in time smooth solution to the Cauchy problem. It allows
to accurately separate the initial data into two classes: one corresponds to a
globally in time smooth solutions, and the other leads to a finite-time blowup.
The influence of electron collision frequency $ \nu $ on the solution is
investigated. It is shown that there is a threshold value, after exceeding
which the regime of damped oscillations is replaced by the regime of monotonic
damping. The set of initial data corresponding to a globally in time smooth
solution of the Cauchy problem expands with increasing $ \nu $, however, at an
arbitrarily large value there are smooth initial data for which the solution
forms a singularity in a finite time, and this time tends to zero as $ \nu $
tends to infinity. The character of the emerging singularities is illustrated
by numerical examples.
