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 : 2016

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 slowly 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 be able to consider potentials growing faster than linearly at infinity, we make use of an additional weight function following the Lyapunov functional approach in (Kolb et al., 2013).
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Dates et versions

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

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Emeric Bouin, Franca Hoffmann, Clément Mouhot. EXPONENTIAL DECAY TO EQUILIBRIUM FOR A FIBRE LAY-DOWN PROCESS ON A MOVING CONVEYOR BELT. 2016. ⟨hal-01315222v2⟩
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