English

Existence of semilinear relaxation shocks

Analysis of PDEs 2009-01-23 v1

Abstract

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 HsH^s spaces.

Keywords

Cite

@article{arxiv.0901.3542,
  title  = {Existence of semilinear relaxation shocks},
  author = {Guy Metivier and Kevin Zumbrun},
  journal= {arXiv preprint arXiv:0901.3542},
  year   = {2009}
}