ERGODICITY AND RATE OF CONVERGENCE FOR A NONSECTORIAL FIBER LAY-DOWN PROCESS

被引：15

作者：

Grothaus, Martin ^{[1
]}

Klar, Axel ^{[1
]}

机构：

[1] Univ Kaiserslautern, Dept Math, D-67653 Kaiserslautern, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2008年 / 40卷 / 03期

关键词：

fiber dynamics; Fokker-Planck equations; Dirichlet forms; ergodicity; rate of convergence;

D O I：

10.1137/070697173

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A stochastic model for the lay-down of fibers on a conveyor belt in the production process of nonwovens is investigated. In particular, convergence of the stochastic process to the stationary solution is proven and estimates on the speed of convergence are given. Numerical results and examples are presented and compared with the analytical estimates on the speed of convergence.

引用

页码：968 / 983

页数：16

共 17 条

[1] On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations [J].

Arnold, A ;

Markowich, P ;

Toscani, G ;

Unterreiter, A .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (1-2) :43-100

[2]

Bogachev V. I., 1997, ANN SCUOLA NORM SUP, V24, P451

[3] Hydrodynamic limit of a Fokker-Planck equation describing fiber lay-down processes [J].

Bonilla, L. L. ;

Gotz, T. ;

Klar, A. ;

Marheineke, N. ;

Wegener, R. .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2007, 68 (03) :648-665

[4]

CONRAD F, CONSTRUCTION ERGODIC

[5] Construction of N-particle Langevin dynamics for H 1,∞-potentials via generalized Dirichlet forms [J].

Conrad, Florian ;

Grothaus, Martin .

POTENTIAL ANALYSIS, 2008, 28 (03) :261-282

[6]

DAPRATO D, 1996, LONDON MATH SOC LECT, V229

[7]

Desvillettes L, 2001, COMMUN PUR APPL MATH, V54, P1, DOI 10.1002/1097-0312(200101)54:1<1::AID-CPA1>3.0.CO

[8]

2-Q

[9]

Douglas J, 1999, NUMER MATH, V83, P353, DOI 10.1007/s002119900075

[10] A stochastic model and associated Fokker-Planck equation for the fiber lay-down process in nonwoven production processes [J].

Goetz, T. ;

Klar, A. ;

Marheineke, N. ;

Wegener, R. .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2007, 67 (06) :1704-1717

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