Existence of semilinear relaxation shocks

We establish existence with sharp rates of decay and distance from the Chapman–Enskog approximation of small-amplitude shock profiles of a class of semilinear relaxation systems including discrete velocity models obtained from Boltzmann and other kinetic equations. Our method of analysis is based on the macro–micro decomposition introduced by Liu and Yu for the study of Boltzmann profiles, but applied to the stationary rather than the time-evolutionary equations. This yields a simple proof by contraction mapping in weighted Hs spaces.

RésuméNous établissons l'existence, avec estimations de convergence de l'approximation de Chapman–Enskog, de profils de choc de systèmes semilinéaires généraux de relaxation.