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MiS Preprint
30/2006

Stability of invariant manifolds in one and two dimensions

Giovanni Bellettini, Anna De Masi, Nicolas Dirr and Errico Presutti

Abstract

We consider the gradient flow associated with a non local 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 a $L^2$ 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.

Received:
Mar 17, 2006
Published:
Mar 17, 2006
MSC Codes:
82C05
Keywords:
nonlocal evolution equation, invariant manifold, Ising model with Kac-potential

Related publications

inJournal
2007 Repository Open Access
Giovanni Bellettini, Anna De Masi, Nicolas Dirr and Errico Presutti

Stability of invariant manifolds in one and two dimensions

In: Nonlinearity, 20 (2007) 3, pp. 537-582