Exponential rate of convergence to equilibrium for a model describing fiber lay-down processes

Schmeiser, Christian; Mouhot, Clément; Klar, Axel; Dolbeault, Jean

Schmeiser, Christian; Mouhot, Clément; Klar, Axel; Dolbeault, Jean (2013), Exponential rate of convergence to equilibrium for a model describing fiber lay-down processes, Applied Mathematics Research Express, 2013, 2, p. 165-175. http://dx.doi.org/10.1093/amrx/abs015

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00658343/fr/

Date

2013

Journal name

Applied Mathematics Research Express

Volume

2013

Number

Publisher

Oxford University Press

Pages

165-175

Abstract (EN)

This paper is devoted to the adaptation of the method developed in [4,3] to a Fokker-Planck equation for fiber lay-down which has been studied in [1,5]. Exponential convergence towards a unique stationary state is proved in a norm which is equivalent to a weighted $L^2$ norm. The method is based on a micro / macro decomposition which is well adapted to the diffusion limit regime.

Subjects / Keywords

exponential rate of convergence; convergence to equilibrium; large time behavior; transport operator; degenerate diffusion; hypoelliptic operators; Poincaré inequality; spectral gap; hypocoercivity; fiber dynamics; Fokker-Planck equation; stochastic differential equations; kinetic equations