Numerical approximation and spectral analysis of infinite-dimensional dynamical systems
03-021 Wolf-Jürgen Beyn, Jens Lorenz.
Stability of viscous profiles: proofs via
dichotomies
In this paper we consider a nonlinear
stability result by
G. Kreiss and H.-O. Kreiss (1998)
for viscous profiles corresponding to strong shocks. The
perturbations have zero mass. A complete proof of the stability
result is given under slightly weaker assumptions than in the
work of Kreiss and Kreiss. We use the theory of exponential
dichotomies for ODEs extensively. A main tool provided by this
theory is a quantitative L
1
perturbation theorem for dichotomies, which yields the delicate
resolvent estimates for s near zero.
