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(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

Kolb, M., Savov, M. and Wübker, A. (2013) (Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process. SIAM Journal on Mathematical Analysis, 45 (1). pp. 1-13. ISSN 0036-1410

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To link to this item DOI: 10.1137/120870724

Abstract/Summary

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:30444
Uncontrolled Keywords:ergodicity, hypoelliptic diffusion process, Lyapunov functions
Publisher:Society for Industrial and Applied Mathematics

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