Validity of the Chapman–Enskog expansion for a class of hyperbolic relaxation systems

This paper presents a validity proof of the Chapman–Enskog expansion for a class of hyperbolic relaxation systems. This class is characterized with a set of conservation–dissipation structural conditions and contains many classical models from mathematical physics. Our main result confirms that the hyperbolic relaxation systems can be well approximated, in the time interval where the corresponding conservation laws have smooth solutions, with the corresponding viscous systems derived by using the Chapman–Enskog expansion.