Hypocoercivity for geometric Langevin equations motivated by fibre lay‐down models arising in industrial application. Issue 4 (25th September 2018)

• Record Type: Journal Article
• Authors: Grothaus, Martin; Mertin, Maximilian; Stilgenbauer, Patrik
• Other Names: Jacob Birgit guestEditor.; Behrndt Jussi guestEditor.; Tretter Christiane guestEditor.; Trunk Carsten guestEditor.
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 41:Issue 4(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-09-25
• Subjects: degenerate diffusion -- fibre dynamics -- hypocoercivity -- Langevin equation; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.201800011
• Languages: English
• ISSNs: 0936-7195

Abstract

Abstract : 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.