Zoology of a non-local cross-diffusion model for two species

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Title: Zoology of a non-local cross-diffusion model for two species
Author(s): Carrillo de la Plata, J
Huang, Y
Schmidtchen, M
Item Type: Journal Article
Abstract: We study a nonlocal two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in [J. A. Carrillo, A. Chertock, and Y. Huang, Commun. Comput. Phys., 17 (2015), pp. 233--258] and explore this new model numerically in terms of its long-time behaviors. Using the so-gained insights, we compute analytical stationary states and travelling pulse solutions for a particular model in the case of attractive-attractive/attractive-repulsive cross-interactions. We show that, as the strength of the cross-diffusivity decreases, there is a transition from adjacent solutions to completely segregated densities, and we compute the threshold analytically for attractive-repulsive cross-interactions. Other bifurcating stationary states with various coexistence components of the support are analyzed in the attractive-attractive case. We find a strong agreement between the numerically and the analytically computed steady states in these particular cases, whose main qualitative features are also present for more general potentials.
Publication Date: 5-Apr-2018
Date of Acceptance: 25-Jan-2018
URI: http://hdl.handle.net/10044/1/56580
DOI: https://dx.doi.org/10.1137/17M1128782
ISSN: 0036-1399
Publisher: Society for Industrial and Applied Mathematics
Start Page: 1078
End Page: 1104
Journal / Book Title: SIAM Journal on Applied Mathematics
Volume: 78
Issue: 2
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Copyright Statement: © 2018 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license (https://creativecommons.org/licenses/by/4.0/)
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
cross-diffusion
nonlocal aggregation-diffusion systems
volume exclusion
AGGREGATION MODEL
INTERACTING POPULATIONS
INTERACTION ENERGY
EMERGENT BEHAVIOR
LOCAL MINIMIZERS
CELL-ADHESION
BLOW-UP
EQUATIONS
DYNAMICS
PARTICLES
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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