Special Session 185: Multiscale Analysis: Geometry and Evolution Problems (mSPACE)

Effective transmission through a thin heterogeneous layer via EDP-convergence
Gianna Goetzmann
University of Augsburg
Germany
Co-Author(s):    Lucas M. Fix, Malte A. Peter, Jan-F. Pietschmann
Abstract:
We study the asymptotic behavior of a Fokker--Planck system in a domain consisting of two bulk regions connected by periodically arranged channels within a thin heterogeneous layer. Both the layer thickness and the distance between the channels scale with $\varepsilon \ll 1$. The system admits a gradient flow formulation with respect to the Boltzmann entropy functional defined on the space of probability measures. Using the notion of EDP-convergence, which is based on the energy--dissipation principle, we aim to derive an effective transmission model in the limit $\varepsilon \to 0$.