Existence of semilinear relaxation shocks

Guy Metivier (1) , Kevin Zumbrun (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Department of Mathematics IU

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 $H^s$ spaces.

Mots clés: shock profiles; relaxation; macro-micro decomposition; Chapman-Enskog approximation; energy methods

Domaines: Equations aux dérivées partielles [math.AP]

Guy Metivier, Kevin Zumbrun. Existence of semilinear relaxation shocks. Journal de Mathématiques Pures et Appliquées, 2009, 92, pp 209--231. ⟨hal-00348427⟩