Preprint 2003-058

Stability of Large-Amplitude Shock Profiles for General Relazation Systems

Corrado Mascia and Kevin Zumbrun

Abstract: Building on previous analyses carried out in [MZ.1, MZ.4], we establish nonlinear $L^1\cap H^2\to L^p$ orbital stability, $2\le p\le \infty$, with sharp rates of decay, of large-amplitude Lax-type shock profiles for a general class of relaxation systems that includes most models in common use, under the necessary conditions of strong spectral stability, i.e., stable point spectrum of the linearized operator about the wave, transversality of the profile, and hyperbolic stability of the associated ideal shock. In particular, our results apply to standard moment closure systems, answering a question left open in [MZ.1]. The argument combines the basic nonlinear stability argument introduced [MZ.1] with an improved ``Goodman-style'' weighted energy estimate similar to that used in [MZ.4] to treat large-amplitude profiles of systems with real viscosity.

Available as Postscript (272 Kbytes) or gzipped PostScript (112 Kbytes; uncompress using gunzip).
Corrado Mascia, <>
Kevin Zumbrun, <>
Publishing information:
in press in Archive for Rational Mechanics and Analysis
Submitted by:
<> September 10 2003.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Thu Sep 11 13:15:57 MEST 2003