Preprint des Projektes: DFG Forschergruppe Spektrale Analysis, asymptotische Verteilungen und stochastische Prozesse

Numerische Approximation und Spektrale Analysis unendlich-dimensionaler Dynamischer Systeme

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.