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Relative Morse indices, Fredholm indices, and group velocities

Sandstede, Bjorn and Scheel, A (2008) Relative Morse indices, Fredholm indices, and group velocities Discrete and Continuous Dynamical Systems A. pp. 139-158.


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We discuss Fredholm properties of the linearization of partial differential equations on cylindrical domains about travelling and modulated waves. We show that the Fredholm index of each such linearization is given by a relative Morse index which depends only on the asymptotic coefficients. Several strategies are outlined that help to compute relative Morse indices using crossing numbers of spatial eigenvalues, and the results are applied to prove the existence of small viscous shock waves in hyperbolic conservation laws upon adding small localized time-periodic source terms.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Scheel, A
Date : 1 January 2008
Additional Information : This is the authors' preprint of an article published in its final form in Discrete and Continuous Dynamical Systems A 20 139-158
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:40
Last Modified : 31 Oct 2017 14:01

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