Journal of Dynamics and Differential Equations

, Volume 14, Issue 3, pp 613–674

Stability of Semi-Discrete Shock Profiles by Means of an Evans Function in Infinite Dimensions

  • Sylvie Benzoni-Gavage

DOI: 10.1023/A:1016391200280

Cite this article as:
Benzoni-Gavage, S. Journal of Dynamics and Differential Equations (2002) 14: 613. doi:10.1023/A:1016391200280


Semi-discrete shock profiles are traveling wave solutions of hyperbolic systems of conservation laws under discretization in space. The existence of semi-discrete shocks has been investigated in earlier papers. Here the spectral stability of those nonlinear waves is addressed, and formulated in terms of a variational delay differential operator. Constructing a generalized Evans function, in infinite dimensions, it is shown how to derive stability criteria. Some examples are given when the criterion is fully explicit, e.g., for extreme Lax shocks. Additionally, connection is made with the alternative approach proposed by Chow, Mallet-Paret, and Shen (Journal of Differential Equations 1998), regarding the stability of traveling waves in general Lattice Dynamical Systems.

Upwind scheme shock wave spectral stability delay differential equation Evans function 

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Sylvie Benzoni-Gavage
    • 1
  1. 1.CNRS & ENS LyonLyon Cedex 07France

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