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Stability of invariant manifolds in one and two dimensions


Reference:

Bellettini, G., De Masi, A., Dirr, N. and Presutti, E., 2007. Stability of invariant manifolds in one and two dimensions. Nonlinearity, 20 (3), pp. 537-582.

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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.

Details

Item Type Articles
CreatorsBellettini, G., De Masi, A., Dirr, N. and Presutti, E.
DOI10.1088/0951-7715/20/3/002
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7006
Additional InformationID number: ISI:000245554900002

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