Seminar 10.12.2010: Peter Szmolyan

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 10.12.2010: Peter Szmolyan

Postby sevcovic » Sun Dec 12, 2010 12:38 pm

Piatok 10.12.2010, 10:40-11:40, F1-326 Friday, December 10, 2010, 10:40-11:40 AM, F1-326

Peter Szmolyan (Technische Universität Wien, Austria)

Spectral stability of viscous shock waves

Abstrakt/Abstract
Results on the stability of viscous shock waves in one and several space dimensions are presented. In the context of Evans function theory a geometric framework is established which allows to show that small amplitude viscous profiles are spectrally stable, i.e. the corresponding linearization along the wave has no eigenvalues λ with Re(λ) ≥ 0, λ ≠ 0. A suitable scaling brings out the slow-fast structure of the problem, which allows a precise description of the behaviour of the stable and unstable spaces in the small amplitude limit by using methods from invariant manifold theory.
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