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

Bouin, Emeric; Hoffmann, Franca; Mouhot, Clément (2017), Exponential decay to equilibrium for a fibre lay-down process on a moving conveyor belt, SIAM Journal on Mathematical Analysis, 49, 4, p. 3233-3251. 10.1137/16M1077490

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01315222
Date
2017
Journal name
SIAM Journal on Mathematical Analysis
Volume
49
Number
4
Publisher
Society for Industrial and Applied Mathematics
Pages
3233-3251
Publication identifier
10.1137/16M1077490
Metadata
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Author(s)
Bouin, Emeric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Hoffmann, Franca
Department of Mathematics [Imperial College London]
Mouhot, Clément
Department of Pure Mathematics and Mathematical Statistics [DPMMS]
Abstract (EN)
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).
Subjects / Keywords
hypocoercivity; rate of convergence; fiber lay-down; existence and uniqueness of a stationary state; perturbation; moving belt

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