Relativistic BGK model of Marle for polyatomic gases near equilibrium

In this paper, we consider the direct application of the relativistic extended thermodynamics theory of polyatomic gases developed in [Ann. Phys. 377 (2017) 414–445] to the relativistic BGK model proposed by Marle. We present the perturbed Marle model around the generalized Jüttner distribution and investigate the properties of the linear operator. Then we prove the global existence and large-time behavior of classical solutions when the initial data is sufficiently close to a global equilibrium.