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Hypocoercivity for geometric Langevin equations motivated by fibre lay‐down models arising in industrial application
Author(s) -
Grothaus Martin,
Mertin Maximilian,
Stilgenbauer Patrik
Publication year - 2018
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201800011
Subject(s) - semigroup , hilbert space , interpretation (philosophy) , homogeneity (statistics) , computer science , exponential function , statistical physics , mathematics , calculus (dental) , mathematical analysis , physics , machine learning , medicine , dentistry , programming language
In this article we review a powerful and fairly simple hypocoercivity method and its application to qualitative analysis of industrially relevant fibre lay‐down models. The hypocoercivity strategy is formulated in an abstract Hilbert space setting with all necessary conditions; we provide some interpretation of these conditions and briefly explain why they are needed to make the machinery working. Once the conditions are fulfilled we gain exponential decay of the strongly continuous semigroup associated to the fibre lay‐down process at an explicitly known rate. We interpret this result as describing for instance homogeneity of nonwoven fibre webs. Primarily, this article portrays the concepts, however it is based on original results by Grothaus and Stilgenbauer, which can be found in the previous studies.