Stability of invariant manifolds in one and two dimensions

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

doi:10.1088/0951-7715/20/3/002

Stability of invariant manifolds in one and two dimensions

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

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (SciVal)

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 language	English
Pages (from-to)	537-582
Number of pages	46
Journal	Nonlinearity
Volume	20
Issue number	3
DOIs	https://doi.org/10.1088/0951-7715/20/3/002
Publication status	Published - 2007

Access to Document

10.1088/0951-7715/20/3/002

Cite this

@article{fab5ce70b727460fab2aedfa3b33999f,

title = "Stability of invariant manifolds in one and two dimensions",

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.",

author = "G Bellettini and {De Masi}, A and N Dirr and E Presutti",

note = "ID number: ISI:000245554900002",

year = "2007",

doi = "10.1088/0951-7715/20/3/002",

language = "English",

volume = "20",

pages = "537--582",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing",

number = "3",

}

TY - JOUR

T1 - Stability of invariant manifolds in one and two dimensions

AU - Bellettini, G

AU - De Masi, A

AU - Dirr, N

AU - Presutti, E

N1 - ID number: ISI:000245554900002

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1088/0951-7715/20/3/002

DO - 10.1088/0951-7715/20/3/002

M3 - Article

SN - 0951-7715

VL - 20

SP - 537

EP - 582

JO - Nonlinearity

JF - Nonlinearity

IS - 3

ER -

Stability of invariant manifolds in one and two dimensions

Abstract

Access to Document

Fingerprint

Cite this