Many of the successful collisional kinetic equations relied heavily on the the assumption that the particles in the gas consist of one atom. But most of the cases, gases consists of polyatomic particles.
Efforts to derive Boltzmann type kinetic models soon confronts with the fact that, since polyatomic molecules can posses arbitrarily complicated structures, it is extremely difficult to obtain the pre- and post-collision velocities in an explicit form.
In search of tractable model equation describing polyatomic gases, a kinetic model equation was suggested as a generalization of the original BGK model of the Boltzmann equation. In this talk, we review several recent results on this model.