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Spectral stability of small-amplitude shock waves.

PDE and Applied Math Seminar

Speaker: Heinrich Friestuhler, Konstanz University, Germany
Location: 1147 MSB
Start time: Wed, Mar 21 2012, 4:10PM

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