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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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 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.

Contact the author per mail Download full preprint 460 KB
Received:
17.03.06
Published:
17.03.06
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
BibTex DOI: 10.1088/0951-7715/20/3/002