Positive similarity solutions for a discrete velocity boltzman coagulation-fragmentation model

We consider the coagulation-fragmentation model of Slemrod and coworkers which is essentially the two-dimensional Broadwell model including inelastic collisions. We construct two classes of similarity solutions (variable =x -t), positive for (- , ): the Rankine-Hugoniot solutions and the scalar Riccati similarity solutions. Previous solutions were built up with positivity along half of thex-axis. For the two classes, we determine in the parameter space, building up the solutions, domains corresponding to positive solutions.