Stability of invariant manifolds in one and two dimensions

G Bellettini, A De Masi, N Dirr, E Presutti

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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 L-2 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.
Original languageEnglish
Pages (from-to)537-582
Number of pages46
JournalNonlinearity
Volume20
Issue number3
DOIs
Publication statusPublished - 2007

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    Bellettini, G., De Masi, A., Dirr, N., & Presutti, E. (2007). Stability of invariant manifolds in one and two dimensions. Nonlinearity, 20(3), 537-582. https://doi.org/10.1088/0951-7715/20/3/002