(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 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.