Stability properties of a class kinetic equations including Boltzmann's equation

A discrete version of Boltzmann's equation is embedded in a class of kinetic equations applying the method of the Moore-Penrose generalized inverse. By means of a family of Lyapunov functionals characterizing the stability properties of this class, we calculate a set of regions of attraction (with respect to the equilibrium distribution) inferring positivity of the solutions and a certain permanence of truncations (e.g. linearization) of the kinetic equations.