Pointwise Green's function bounds and stability of relaxation shocks
Abstract
We establish sharp pointwise Green's function bounds and consequent linearized and nonlinear stability for smooth traveling front solutions, or relaxation shocks, of general hyperbolic relaxation systems of dissipative type, under the necessary assumptions ([G,Z.1,Z.4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave, and hyperbolic stability of the corresponding ideal shock of the associated equilibrium system. This yields, in particular, nonlinear stability of weak relaxation shocks of the discrete kinetic Jin--Xin and Broadwell models. The techniques of this paper should have further application in the closely related case of traveling waves of systems with partial viscosity, for example in compressible gas dynamics or MHD.
Cite
@article{arxiv.math/0107107,
title = {Pointwise Green's function bounds and stability of relaxation shocks},
author = {Corrado Mascia and Kevin Zumbrun},
journal= {arXiv preprint arXiv:math/0107107},
year = {2007}
}
Comments
120 pages. Changes since original submission. Corrected typos, esp. energy estimates of Section 7, corrected bad forward references, expanded Remark 1.17, end of introduction