On the Maxwell problem (Q613752)

The authors study the long-time behavior of global smooth solution to hyperbolic regularizations of conservation laws (i.e., systems of conservation laws with relaxation). They justify the Chapman-Enskog projection onto the phase space of conservative variables, which determines an attractive manifold of special global smooth solutions. The case of moment approximations for kinetic equations is particularly studied. In this case the authors construct the Chapman-Enskog projection for small initial data and describe its properties. It is shown that the existence conditions for the Chapman-Enskog projection can be expressed in terms of the solvability of the Riccati matrix equation with parameter.