Stability of small-amplitude shock profiles of symmetric hyperbolic-parabolic systems

Combining pointwise Green's function bounds obtained in a companion paper [36] with earlier, spectral stability results obtained in [16], we establish nonlinear orbital stability of small-amplitude Lax-type viscous shock profiles for the class of dissipative symmetric hyperbolic-parabolic systems identified by Kawashima [20], notably including compressible Navier-Stokes equations and the equations of magnetohydrodynamics, obtaining sharp rates of decay in L-p with respect to small L-1 boolean AND H-3 perturbations, 2 less than or equal to p less than or equal to infinity. Our analysis extends and somewhat refines the approach introduced in [35] to treat stability of relaxation profiles. (C) 2004 Wiley Periodicals, Inc.