Flow characteristics in a crowded transport model

Burger M, Pietschmann JF (2016)

Publication Type: Journal article

Publication year: 2016


Publisher: Institute of Physics Publishing

Book Volume: 29

Pages Range: 3528-3550

Issue: 11

DOI: 10.1088/0951-7715/29/11/3528


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.

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


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

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