Splitting schemes and segregation in reaction cross-diffusion systems
One of the most fascinating phenomenon observed in reaction diffusion systems is the emergence of segregated solutions, i.e., population densities with disjoint supports. We analyze such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data...
| Main Authors: | , , , |
|---|---|
| Format: | Journal article |
| Sprog: | English |
| Udgivet: |
Society for Industrial and Applied Mathematics
2018
|
| _version_ | 1826301599001083904 |
|---|---|
| author | Carrillo, JA Fagioli, S Santambrogio, F Schmidtchen, M |
| author_facet | Carrillo, JA Fagioli, S Santambrogio, F Schmidtchen, M |
| author_sort | Carrillo, JA |
| collection | OXFORD |
| description | One of the most fascinating phenomenon observed in reaction diffusion systems is the emergence of segregated solutions, i.e., population densities with disjoint supports. We analyze such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction of their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to prove conservation of segregation for initially segregated data even in the presence of vacuum. |
| first_indexed | 2024-03-07T05:34:50Z |
| format | Journal article |
| id | oxford-uuid:e388659a-3284-4451-b3aa-140ae98d9d2d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:34:50Z |
| publishDate | 2018 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:e388659a-3284-4451-b3aa-140ae98d9d2d2022-03-27T10:09:44ZSplitting schemes and segregation in reaction cross-diffusion systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e388659a-3284-4451-b3aa-140ae98d9d2dEnglishSymplectic ElementsSociety for Industrial and Applied Mathematics 2018Carrillo, JAFagioli, SSantambrogio, FSchmidtchen, MOne of the most fascinating phenomenon observed in reaction diffusion systems is the emergence of segregated solutions, i.e., population densities with disjoint supports. We analyze such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction of their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to prove conservation of segregation for initially segregated data even in the presence of vacuum. |
| spellingShingle | Carrillo, JA Fagioli, S Santambrogio, F Schmidtchen, M Splitting schemes and segregation in reaction cross-diffusion systems |
| title | Splitting schemes and segregation in reaction cross-diffusion systems |
| title_full | Splitting schemes and segregation in reaction cross-diffusion systems |
| title_fullStr | Splitting schemes and segregation in reaction cross-diffusion systems |
| title_full_unstemmed | Splitting schemes and segregation in reaction cross-diffusion systems |
| title_short | Splitting schemes and segregation in reaction cross-diffusion systems |
| title_sort | splitting schemes and segregation in reaction cross diffusion systems |
| work_keys_str_mv | AT carrilloja splittingschemesandsegregationinreactioncrossdiffusionsystems AT fagiolis splittingschemesandsegregationinreactioncrossdiffusionsystems AT santambrogiof splittingschemesandsegregationinreactioncrossdiffusionsystems AT schmidtchenm splittingschemesandsegregationinreactioncrossdiffusionsystems |