Existence of semilinear relaxation shocks
Langue
en
Article de revue
Ce document a été publié dans
Journal de Mathématiques Pures et Appliquées. 2009, vol. 92, p. pp 209--231
Elsevier
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
shock profiles
relaxation
macro-micro decomposition
Chapman-Enskog approximation
energy methods
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