The Conley index along heteroclinic trajectories of reaction-diffusion equations
type: Item
instance of: scholarly article
title: The Conley index along heteroclinic trajectories of reaction-diffusion equations
zbMATH Open document ID: 1263.35144
published in: Journal of Differential Equations
publication date: 2012-03-29T00:00:00Z
review text: It is well known that hyperbolic equilibria of reaction-diffusion equations have the homotopy Conley index of a pointed sphere, the dimension of which is the Morse index of the equilibrium. A similar result concerning the homotopy Conley index along heteroclinic solutions of ordinary differential equations under the assumption that the respective stable and unstable manifolds intersect transversally, is due to \textit{C. McCord} [Trans. Am. Math. Soc. 307, No. 1, 195--203 (1988; Zbl 0646.34056)]. This result has recently been generalized by \textit{E. N. Dancer} [Bull. Aust. Math. Soc. 80, No. 3, 510--520 (2009; Zbl 1181.35137)] to some reaction-diffusion equations by using finite-dimensional approximations. In this paper the author extends McCord's result to reaction-diffusion equations. Additionally, an error in the original proof is pointed out and corrected.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 47J35
Mathematics Subject Classification ID: 37C29
zbMATH DE Number: 6019797
zbMATH Keywords: connecting orbits
author: Axel Jänig
MaRDI profile type: Publication
full work available at URL: j.jde.2012.01.012
OpenAlex ID: W2074595067
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DOI: 10.1016/J.JDE.2012.01.012
description: scientific article; zbMATH DE number 6019797