Abstract
The linear stability of semi-discrete (i.e. continuous in time and discrete in space) shock profiles is investigated. It is encoded in the spectrum of a retarded differential operator. In order to obtain necessary stability conditions, an Evans function based on the (infinite dimensional) eigenvalue equations and their adjoints is constructed. The method is then applied to the cases of Lax shocks and of undercompressive shocks.
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Benzoni-Gavage, S. (2001). On the Stability of Large Amplitude Semi-discrete Shock Profiles by Means of an Evans Function in Infinite Dimensions. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_16
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DOI: https://doi.org/10.1007/978-3-0348-8370-2_16
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