Abstract
The Conley index is a double-edged sword: if it is ever shown to be nontrivial, then this implies the existence of an orbit which stays in the isolating neighborhood for all time; in this sense it gives an existence theorem. On the other hand, being a Morse-type index, it also carries stability information concerning the isolated invariant set. In this chapter we shall illustrate both of these properties for a special class of solutions of partial differential equations called travelling waves.
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© 1983 Springer-Verlag New York Inc.
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Smoller, J. (1983). Travelling Waves. In: Shock Waves and Reaction—Diffusion Equations. Grundlehren der mathematischen Wissenschaften, vol 258. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0152-3_24
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DOI: https://doi.org/10.1007/978-1-4684-0152-3_24
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0154-7
Online ISBN: 978-1-4684-0152-3
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