Exponential rate of convergence to equilibrium for a model describing fiber lay-down processes
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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00658343/fr/
Journal nameApplied Mathematics Research Express
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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 / Keywordsexponential 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
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