The nonlinear BGK model-a derivation and two applications

Employing a single well defined approximation, a derivation is given of the nonlinear BGK model. The model is applied to the formulation of equations governing the temporal and spatial variation of macroscopic parameters in the regime where changes in these parameters within a mean free path cannot be neglected. Using the model, an extension is given of earlier results concerning the sign of successive time derivatives of the entropy.