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SUMMARY:Rate of Convergence to Equilibrium for a Model describing Fibre La
 y-down Processes on a Moving Conveyor Belt - Franca Hoffmann (CCA - Imperi
 al College)
DTSTART:20150304T160000Z
DTEND:20150304T170000Z
UID:TALK57704@talks.cam.ac.uk
CONTACT:Davide Piazzoli
DESCRIPTION:We study the hypocoercivity properties of a kinetic Fokker-Pla
 nck equation modelling the fibre lay-down process in the production of non
 -woven textiles. Under suitable assumptions on the potential describing th
 e coiling properties of the fibres\, we establish existence and uniqueness
  of a global Gibbs state and determine the rate of convergence of solution
 s in a suitably weighted L^2 space using only hypocoercivity techniques. T
 he method is based on a micro / macro decomposition which is well adapted 
 to the diffusion limit regime. Our result is an extension of the method us
 ed by Dolbeault et al. who assumed a stationary conveyor belt. For technic
 al applications in the production process of non-wovens however\, one  is 
 interested in a model including the movement of the conveyor belt\, in whi
 ch case the global Gibbs state is not known explicitly. This can be addres
 sed by proving a stronger hypocoercivity estimate for solutions of the kin
 etic Fokker-Planck equation. This is a joint work with Clément Mouhot and
  Emeric Bouin.
LOCATION:MR14\, Centre for Mathematical Sciences
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