Preprint 2002-058

Pointwise Green's Function Bounds for Shock Profiles of Systems with Real Viscosity

Corrado Mascia and Kevin Zumbrun

Abstract: Following the pointwise semigroup approach of [ZH,MZ.1], we establish sharp pointwise Green's function bounds and consequent linearized stability for viscous shock profiles of general hyperbolic--parabolic systems of conservation laws of dissipative type, under the necessary assumptions ([Z.1,Z.3--4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave; transversality of the connecting profile; and hyperbolic stability of the corresponding ideal shock of the associated inviscid system, with no additional assumptions on the structure or strength of the shock. These bounds are used in a companion paper [MZ.2] to establish nonlinear stability of small-amplitude Lax shocks of symmetrizable hyperbolic--parabolic systems.

Available as PostScript (832 Kbytes) or gzipped PostScript (304 Kbytes; uncompress using gunzip).
Corrado Mascia, <>
Kevin Zumbrun, <>
Publishing information:
Submitted by:
<> December 23 2002.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 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: Mon Dec 30 11:00:24 MET 2002