Metastability for the Ginzburg–Landau

Nils Berglund

Description

Niveau: Supérieur
Metastability for the Ginzburg–Landau equation with space-time noise Nils Berglund MAPMO, Universite d'Orleans CNRS, UMR 6628 and Federation Denis Poisson Collaborators: Florent Barret, Ecole Polytechnique, Palaiseau Bastien Fernandez, CPT, CNRS, Marseille Barbara Gentz, University of Bielefeld Grenoble, 12 march 2009

• stationary solution


• noise


• ginzburg–landau equation


• time noise

Sujets

• Barret
• Poisson
• Berglund
• École polytechnique
• Fernández
• Ginzburg?Landau theory

Informations

• Publié par: chaeh
• Nombre de lectures: 14
• Langue: English

Extrait

Metastability for the Ginzburg–Landau

equation with space-time noise

Nils Berglund MAPMO,Universit´ed’Orl´eans CNRS,UMR6628andFe´de´rationDenisPoisson www.univ-orleans.fr/mapmo/membres/berglund

Collaborators: Florent Barret , Ecole Polytechnique, Palaiseau Bastien Fernandez , CPT, CNRS, Marseille Barbara Gentz , University of Bielefeld

Grenoble, 12 march 2009

Ginzburg–Landau equation

∂ t u ( x, t ) = ∂ xx u ( x, t ) + u ( x, t ) − u ( x, t )

x∈[0,]L,u(,x)t∈

• Periodic b.c. • Neumann b.c.

R

errpseents.e.g

3

amng

∂ x u (0 , t ) = ∂ x u ( L, t ) = 0

teisaitno

1

Ginzburg–Landau equation

∂ t u ( x, t ) = ∂ xx u ( x, t ) + u ( x, t ) − u ( x, t ) 3 + noise

x∈[0,]L,u(,x)t∈

R

errpesentse.g.magn

• Periodic b.c. • Neumann b.c. ∂ x u (0 , t ) = ∂ x u ( L, t ) = 0

Noise : weak, white in space and time

etisaitno

1-a

Ginzburg–Landau equation

∂ t u ( x, t ) = ∂ xx u ( x, t ) + u ( x, t ) − u ( x, t ) 3 + noise

x ∈ [0 , L ], u ( x, t ) ∈ R

errpseetns.eg.amgn

• Periodic b.c. • Neumann b.c. ∂ x u (0 , t ) = ∂ x u ( L, t ) = 0

Noise : weak, white in space and time

Deterministic system is gradient

teisation

∂ t u ( x, t ) = ∂ xx u ( x, t ) + u ( x, t ) − u ( x, t ) 3 = − ∂ ∂ δ V x [ u ( ∙ , t )] V [ u ] = Z 0 L  1 2 u 0 ( x ) 2 − 2 1 u ( x ) 2 + 4 1 u ( x ) 4  d x

1-b