Zoology of a nonlocal cross-diffusion model for two species
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 nume...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial & Applied Mathematics
2018
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| _version_ | 1797075078509232128 |
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| author | Huang, Y Schmidtchen, M |
| author_facet | Huang, Y Schmidtchen, M |
| author_sort | Huang, Y |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T23:45:11Z |
| format | Journal article |
| id | oxford-uuid:70a7af72-716d-4fda-9bc9-14c348a40619 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:45:11Z |
| publishDate | 2018 |
| publisher | Society for Industrial & Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:70a7af72-716d-4fda-9bc9-14c348a406192022-03-26T19:38:37ZZoology of a nonlocal cross-diffusion model for two speciesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:70a7af72-716d-4fda-9bc9-14c348a40619EnglishSymplectic ElementsSociety for Industrial & Applied Mathematics2018Huang, YSchmidtchen, MWe 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. |
| spellingShingle | Huang, Y Schmidtchen, M Zoology of a nonlocal cross-diffusion model for two species |
| title | Zoology of a nonlocal cross-diffusion model for two species |
| title_full | Zoology of a nonlocal cross-diffusion model for two species |
| title_fullStr | Zoology of a nonlocal cross-diffusion model for two species |
| title_full_unstemmed | Zoology of a nonlocal cross-diffusion model for two species |
| title_short | Zoology of a nonlocal cross-diffusion model for two species |
| title_sort | zoology of a nonlocal cross diffusion model for two species |
| work_keys_str_mv | AT huangy zoologyofanonlocalcrossdiffusionmodelfortwospecies AT schmidtchenm zoologyofanonlocalcrossdiffusionmodelfortwospecies |