## Publications |

C. Fries: Stability of Viscous Shock Waves.

Doctoral thesis, RWTH Aachen, Shaker Verlag Aachen, 1999,

ISBN 3-8265-4993-7.

## Abstract |

In this thesis we consider small-amplitude viscous shock waves
associated with a possibly *non-convex* mode (i.e., a not
necessarily "genuinely nonlinear field") and prove their
time-asymptotic stability towards sufficiently small perturbations
of not necessarily vanishing mass. We thus extend the result of
[SX] to the case of non-convex modes and the result of [F1]
to the case of non-zero mass perturbations.

**References**- [F1]
- C. Fries: Nonlinear asymptotic stability of general small-amplitude
viscous Laxian shock waves,
*J. Differ. Equations***146**(1998), 185-202. - [SX]
- A. Szepessy, Z. Xin: Nonlinear stability of viscous shock
waves,
*Arch. Rational Mech. Anal.***122**(1993), 53-103.