Phase transitions and bump solutions of the Keller-Segel model with volume exclusion
We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myriad of symmetric and asymmetric stationary states w...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Society for Industrial and Applied Mathematics
2020
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| _version_ | 1797060601969639424 |
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| author | Carrillo, JA Chen, X Wang, Q Wang, Z Zhang, L |
| author_facet | Carrillo, JA Chen, X Wang, Q Wang, Z Zhang, L |
| author_sort | Carrillo, JA |
| collection | OXFORD |
| description | We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myriad of symmetric and asymmetric stationary states whose stability properties are mostly studied via free energy decreasing numerical schemes. The metastability behavior and staircased free energy decay are also illustrated via these numerical simulations. |
| first_indexed | 2024-03-06T20:19:24Z |
| format | Journal article |
| id | oxford-uuid:2d469d9f-abf7-4295-b47f-2a67e91a12dd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:19:24Z |
| publishDate | 2020 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:2d469d9f-abf7-4295-b47f-2a67e91a12dd2022-03-26T12:41:55ZPhase transitions and bump solutions of the Keller-Segel model with volume exclusionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2d469d9f-abf7-4295-b47f-2a67e91a12ddEnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2020Carrillo, JAChen, XWang, QWang, ZZhang, LWe show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myriad of symmetric and asymmetric stationary states whose stability properties are mostly studied via free energy decreasing numerical schemes. The metastability behavior and staircased free energy decay are also illustrated via these numerical simulations. |
| spellingShingle | Carrillo, JA Chen, X Wang, Q Wang, Z Zhang, L Phase transitions and bump solutions of the Keller-Segel model with volume exclusion |
| title | Phase transitions and bump solutions of the Keller-Segel model with volume exclusion |
| title_full | Phase transitions and bump solutions of the Keller-Segel model with volume exclusion |
| title_fullStr | Phase transitions and bump solutions of the Keller-Segel model with volume exclusion |
| title_full_unstemmed | Phase transitions and bump solutions of the Keller-Segel model with volume exclusion |
| title_short | Phase transitions and bump solutions of the Keller-Segel model with volume exclusion |
| title_sort | phase transitions and bump solutions of the keller segel model with volume exclusion |
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