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Discrete and continuum links to a nonlinear coupled transport problem of interacting populations

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Title: Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
Authors: Duong, MH
Muntean, A
Richardson, OM
Item Type: Journal Article
Abstract: We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.
Issue Date: 1-Jul-2017
Date of Acceptance: 1-Feb-2017
URI: http://hdl.handle.net/10044/1/60084
DOI: https://dx.doi.org/10.1140/epjst/e2017-70009-y
ISSN: 1951-6355
Publisher: SPRINGER HEIDELBERG
Start Page: 2345
End Page: 2357
Journal / Book Title: EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
Volume: 226
Issue: 10
Copyright Statement: © 2017 The Author(s). Open Access. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics
DIFFUSION
EQUATION
SYSTEMS
01 Mathematical Sciences
02 Physical Sciences
Applied Physics
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2017-02-16
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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