C. Fries: Stability of Viscous Shock Waves.
Doctoral thesis, RWTH Aachen, Shaker Verlag Aachen, 1999,
ISBN 3-8265-4993-7.


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.

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