Exact solutions of the Boltzmann equation in the VHP model with removal interaction

The linear and nonlinear Boltzmann equation for very hard particles (VHP) is considered in the case when the collision between two particles may lead not only to elastic scattering, but also to a removal event with the disappearance of the molecules. The extended transport equation is solved for arbitrary initial distributions. The computations are carried out explicitly for a special class of initial distributions and for various removal rates. The results are demonstrated graphically. Finally, source terms fulfilling physically reasonable conditions are introduced into the VHP model, and the time-dependent particle number is calculated.