Flow characteristics in a crowded transport model

Journal article


Publication Details

Author(s): Burger M, Pietschmann JF
Journal: Nonlinearity
Publisher: Institute of Physics Publishing
Publication year: 2016
Volume: 29
Pages range: 3528-3550
ISSN: 0951-7715


Abstract

The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of solutions. We use a derivation from a microscopic asymmetric exclusion process and its extension to particles entering or leaving on the boundaries. This leads to specific Robin-type boundary conditions for inflow and outflow, respectively. For the stationary equation we prove the existence of solutions in a suitable set-up. Moreover, we investigate the flow characteristics for a small diffusion parameter ϵ, which yields the occurrence of a maximal current phase in addition to well-known one-sided boundary layer effects for linear driftdiffusion problems. In a 1D set-up we provide rigorous estimates in terms of ϵ, which confirm three different phases. Finally, we derive a numerical approach to solve the problem also in multiple dimensions.


External institutions with authors

Technische Universität Darmstadt
Westfälische Wilhelms-Universität (WWU) Münster


How to cite

APA:
Burger, M., & Pietschmann, J.-F. (2016). Flow characteristics in a crowded transport model. Nonlinearity, 29, 3528-3550. https://dx.doi.org/10.1088/0951-7715/29/11/3528

MLA:
Burger, Martin, and Jan-Frederik Pietschmann. "Flow characteristics in a crowded transport model." Nonlinearity 29 (2016): 3528-3550.

BibTeX: 

Last updated on 2018-03-12 at 09:23