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Spectral stability of small-amplitude shock waves.
PDE & Applied Mathematics| Speaker: | Heinrich Friestuhler, Konstanz University, Germany |
| Location: | 1147 MSB |
| Start time: | Wed, Mar 21 2012, 4:10PM |
Description
Abstract: The talk discusses spectral stability of viscous and inviscid shock in
several space variables. The spectrum of small-amplitude waves
associated with a genuinely nonlinear Metivier convex mode is shown to
be strictly stable if the mode is extreme (i. e., it corresponds to the
largest or smallest characteristic speed). It is also shown that under
otherwise identical assumptions, stability is not always strict if the
mode is not extreme.
[1] H. Freist\"uhler and P. Szmolyan: Spectral stability of
small-amplitude viscous shock waves in several space dimensions.
Arch. Ration. Mech. Anal. 195 (2010), 353–373.
[2] H. Freist\"uhler and P. Szmolyan: The Lopatinski determinant of
small shocks may vanish. arXiv:1102.4279