Asymptotic properties of the inelastic Kac model

We discuss the asymptotic behavior of certain models of dissipative systems
obtained from a suitable modification of Kac caricature of a Maxwellian gas. It
is shown that global equilibria different from concentration are possible if the
energy is not finite. These equilibria are distributed like stable laws, and attract
initial densities which belong to the normal domain of attraction. If the initial
density is assumed of finite energy, with higher moments bounded, it is shown
that the solution converges for large-time to a profile with power law tails.
These tails are heavily dependent of the collision rule.