Kinetic decomposition for kinetic models of BGK type

In this paper, we consider kinetic models of BGK type which describe the scalar conservation law at the microscopic scale. We use new technique developed in Comm. Partial Differential Equations 27 (2002) 1229 in order to get the convergence. First, we obtain the approximate transport equation for the given kinetic models of BGK type. Then using the averaging lemma, we obtain the convergence. This paper shows how to relate the given kinetic model with the averaging lemma to get the convergence.