Exponential decay to equilibrium for a fibre lay-down process on a moving conveyor belt - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

Exponential decay to equilibrium for a fibre lay-down process on a moving conveyor belt

Résumé

We show existence and uniqueness of a stationary state for a kinetic Fokker-Planck equation modelling the fibre lay-down process in the production of non-woven textiles. Following a micro-macro decomposition, we use hypocoercivity techniques to show exponential convergence to equilibrium with an explicit rate assuming the conveyor belt moves slow enough. This work is an extension of (Dolbeault et al., 2013), where the authors consider the case of a stationary conveyor belt. Adding the movement of the belt, the global Gibbs state is not known explicitly. We thus derive a more general hypocoercivity estimate from which existence, uniqueness and exponential convergence can be derived. To treat the same class of potentials as in (Dolbeault et al., 2013), we make use of an additional weight function following the Lyapunov functional approach in (Kolb et al., 2013).
Fichier principal
Vignette du fichier
HypobeltHAL.pdf (362.27 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01315222 , version 1 (12-05-2016)
hal-01315222 , version 2 (05-07-2016)
hal-01315222 , version 3 (14-04-2017)

Identifiants

Citer

Emeric Bouin, Franca Hoffmann, Clément Mouhot. Exponential decay to equilibrium for a fibre lay-down process on a moving conveyor belt. 2017. ⟨hal-01315222v3⟩
666 Consultations
113 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More