Uniqueness of stationary states for singular Keller–Segel type models
We consider a generalised Keller–Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are more singular than Newtonian interaction. We show uniqueness of stationary states (if they exist) in any dimension both in the dif...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2020
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| _version_ | 1826296164913250304 |
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| author | Calvez, V Carrillo, JA Hoffmann, F |
| author_facet | Calvez, V Carrillo, JA Hoffmann, F |
| author_sort | Calvez, V |
| collection | OXFORD |
| description | We consider a generalised Keller–Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are more singular than Newtonian interaction. We show uniqueness of stationary states (if they exist) in any dimension both in the diffusion-dominated regime and in the fair-competition regime when attraction and repulsion are in balance. As stationary states are radially symmetric decreasing, the question of uniqueness reduces to the radial setting. Our key result is a sharp generalised Hardy–Littlewood–Sobolev type functional inequality in the radial setting. |
| first_indexed | 2024-03-07T04:12:08Z |
| format | Journal article |
| id | oxford-uuid:c82cdc6a-00e8-4b83-9ea5-fe3d22b97a81 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:12:08Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:c82cdc6a-00e8-4b83-9ea5-fe3d22b97a812022-03-27T06:50:25ZUniqueness of stationary states for singular Keller–Segel type modelsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c82cdc6a-00e8-4b83-9ea5-fe3d22b97a81EnglishSymplectic ElementsElsevier2020Calvez, VCarrillo, JAHoffmann, FWe consider a generalised Keller–Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are more singular than Newtonian interaction. We show uniqueness of stationary states (if they exist) in any dimension both in the diffusion-dominated regime and in the fair-competition regime when attraction and repulsion are in balance. As stationary states are radially symmetric decreasing, the question of uniqueness reduces to the radial setting. Our key result is a sharp generalised Hardy–Littlewood–Sobolev type functional inequality in the radial setting. |
| spellingShingle | Calvez, V Carrillo, JA Hoffmann, F Uniqueness of stationary states for singular Keller–Segel type models |
| title | Uniqueness of stationary states for singular Keller–Segel type models |
| title_full | Uniqueness of stationary states for singular Keller–Segel type models |
| title_fullStr | Uniqueness of stationary states for singular Keller–Segel type models |
| title_full_unstemmed | Uniqueness of stationary states for singular Keller–Segel type models |
| title_short | Uniqueness of stationary states for singular Keller–Segel type models |
| title_sort | uniqueness of stationary states for singular keller segel type models |
| work_keys_str_mv | AT calvezv uniquenessofstationarystatesforsingularkellersegeltypemodels AT carrilloja uniquenessofstationarystatesforsingularkellersegeltypemodels AT hoffmannf uniquenessofstationarystatesforsingularkellersegeltypemodels |