  We study the influence of the factor of electron-ion collisions on the
solution of the Cauchy problem in the one-dimensional relativistic model of
cold plasma and show that, depending on their intensity and initial data, two
scenarios are possible: either the solution remains smooth and stabilizes to a
stationary state, or during a finite time the oscillations blowup.
  In contrast to the nonrelativistic model, when exact conditions can be
obtained separating the two behaviors, in a much more complicated relativistic
situation, it turns out to be possible to analytically estimate from below the
time during which the existence of a smooth solution and the guaranteed number
of oscillations during this time. In addition, we show that in contrast to the
relativistic case without taking into account collisions, when oscillations
corresponding to arbitrarily small deviations from the zero equilibrium
position blow up, the presence of electron collisions can suppress the blow-up
of sufficiently small oscillations. Further, based on the analysis of
characteristics, a numerical algorithm is constructed, the order of accuracy of
which is determined only by the smoothness of the initial data. Numerical
experiments are presented to illustrate the theoretical results. The initial
conditions are chosen as reasonably as possible from the point of view of
full-scale physical experiments.
