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Stability of invariant manifolds in one and two dimensions

Bellettini, G., De Masi, A., Dirr, Nicolas P. 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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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: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: IOP Publishing
ISSN: 0951-7715
Last Modified: 04 Jun 2017 02:52

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