The exact distribution of velocities for the 1D pseudo-Maxwell model

In this brief section we discuss the pseudo-Maxwell model, which disregards the exact kinetic kernel $\vert v-v'\vert$ in the Boltzmann equation and therefore accounts for a flat scattering cross section. We give an exact asymptotic scaling solution (``Baldassarri solution'' [14,12,13]) of the model in $d=1$. The problem in $d=2$, has been discussed by Bobylev and co-workers [33]. The found solutions are compared with the granular models discussed before.