From the Boltzmann equation to generalized kinetic models in applied sciences

This paper deals with kinetic-type (Boltzmann) modelling and with the analysis of mathematical problems related to the application of models. The line followed in the organization of the paper starts from a concise report on Boltzmann equation and goes to the analysis of models linked to this fundamental equation on nonequilibrium statistical mechanics. The paper aims to provide a guideline towards modelling systems of interest in applied sciences by means of kinetic-type equations.