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Erschienen in:
1994 | OriginalPaper | Buchkapitel
Travelling Waves
verfasst von : Joel Smoller
Erschienen in: Shock Waves and Reaction—Diffusion Equations
Verlag: Springer New York
Enthalten in: Professional Book Archive
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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.