2021/02/09 by Daniel Karrasch, Karrasch, Daniel, Nathanael Schilling +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35P15 #47D07 #53B50 #76R99 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory (math.SP) #math-ph #math.AP #math.DG #math.DS #math.MP #math.SP #msc:35P15 #msc:47D07 #msc:53B50 #msc:76R99
paper · pdf · doi:10.48550/arxiv.2102.04777
38 pages, submitted
openalex publication_date 2021/02/09 · arxiv created 2021/03/19 · arxiv updated 2021/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study mass preserving transport of passive tracers in the low-diffusivity limit using Lagrangian coordinates. Over finite-time intervals, the solution-operator of the nonautonomous diffusion equation is approximated by that of a time-averaged diffusion equation. We show that leading order asymptotics that hold for functions [Krol, 1991] extend to the dominant nontrivial singular value. This answers questions raised in [Karrasch & Keller, 2020]. The generator of the time-averaged diffusion/heat semigroup is a Laplace operator associated to a weighted manifold structure on the material manifold. We show how geometrical properties of this weighted manifold directly lead to physical transport quantities of the nonautonomous equation in the low-diffusivity limit.