Long-time behaviour of Langevin-type dynamics on Riemannian manifolds and scaling limits

  • The thesis investigates the phenomenon of hypocoercivity for Langevin-type equations on manifolds via a powerful abstract Hilbert space method. In applications, hypocoercivity experienced by the semigroup can be used to find optimal parameters for the production of nonwoven fleeces. Furthermore, the last chapter introduces a new scaling limit technique: Employing the concept of so-called stratifolds we can show Kuwae-Shioya-Mosco convergence of anisotropic 3D fibre lay-down models to an isotropic 2D model.

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Author:Maximilian MertinORCiD
Advisor:Martin GrothausORCiD
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2022/11/15
Year of Publication:2022
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2022/08/04
Date of the Publication (Server):2022/11/16
Tag:Langevin equation; Mosco convergence; fibre lay-down dynamics; hypocoercivity; semisprays; stratifolds
Number of page:X, 139
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):46-XX FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx) / 46Nxx Miscellaneous applications of functional analysis [See also 47Nxx] / 46N20 Applications to differential and integral equations
53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Zxx Applications to physics / 53Z05 Applications to physics
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)