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Axel Jänig

The Morse complex for reaction-diffusion equations

Universität Rostock, 2011

Abstract: The singular homology of a compact smooth Riemannian manifold can be described by means of its Morse-Smale-Witten chain complex. There are proofs of this which rely on Conley index theory. We generalize these ideas to cover a class of semilinear parabolic equations, notably reaction-diffusion equations. Finally, one obtains a Morse complex for suitable isolated invariant sets.

doctoral thesis   free access    


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