Stability of invariant manifolds in one and two dimensions

Bellettini, G., De Masi, A., Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367 and Presutti, E. 2007. Stability of invariant manifolds in one and two dimensions. Nonlinearity 20 (3) , pp. 537-582. 10.1088/0951-7715/20/3/002

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Abstract

We consider the gradient flow associated with a nonlocal free energy functional and extend to such a case results obtained for the Allen–Cahn equation on 'slow motions on invariant manifolds'. The manifolds in question are time-invariant one-dimensional curves in an L2 space which connect the two ground states (interpreted as the pure phases of the system) to the first excited state (interpreted as a diffuse interface). Local and structural stability of the manifolds are proved and applications to the characterization of optimal tunnelling are discussed.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	IOP Publishing
ISSN:	0951-7715
Last Modified:	18 Oct 2022 13:13
URI:	https://orca.cardiff.ac.uk/id/eprint/13079

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