Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime
We first show the existence of a unique global minimizer of the free energy for all masses associated with a nonlinear diffusion version of the classical Keller-Segel model when the diffusion dominates over the attractive force of the chemoattractant. The strategy uses an approximation of the variat...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Indiana University Mathematics Journal
2018
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| _version_ | 1826261192629288960 |
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| author | Carrillo, JA Sugiyama, Y |
| author_facet | Carrillo, JA Sugiyama, Y |
| author_sort | Carrillo, JA |
| collection | OXFORD |
| description | We first show the existence of a unique global minimizer of the free energy for all masses associated with a nonlinear diffusion version of the classical Keller-Segel model when the diffusion dominates over the attractive force of the chemoattractant. The strategy uses an approximation of the variational problem in the whole space by the minimization problem posed on bounded balls with large radii. We show that all stationary states in a wide class coincide up to translations with the unique global minimizer of the free energy, which is compactly supported, radially decreasing, and smooth inside its support. Our results complement and show alternative proofs with respect to [27, 30, 36]. |
| first_indexed | 2024-03-06T19:17:40Z |
| format | Journal article |
| id | oxford-uuid:18f5b35b-cb65-4c3b-99e5-b10f301160ce |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:17:40Z |
| publishDate | 2018 |
| publisher | Indiana University Mathematics Journal |
| record_format | dspace |
| spelling | oxford-uuid:18f5b35b-cb65-4c3b-99e5-b10f301160ce2022-03-26T10:46:11ZCompactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regimeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:18f5b35b-cb65-4c3b-99e5-b10f301160ceEnglishSymplectic ElementsIndiana University Mathematics Journal2018Carrillo, JASugiyama, YWe first show the existence of a unique global minimizer of the free energy for all masses associated with a nonlinear diffusion version of the classical Keller-Segel model when the diffusion dominates over the attractive force of the chemoattractant. The strategy uses an approximation of the variational problem in the whole space by the minimization problem posed on bounded balls with large radii. We show that all stationary states in a wide class coincide up to translations with the unique global minimizer of the free energy, which is compactly supported, radially decreasing, and smooth inside its support. Our results complement and show alternative proofs with respect to [27, 30, 36]. |
| spellingShingle | Carrillo, JA Sugiyama, Y Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime |
| title | Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime |
| title_full | Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime |
| title_fullStr | Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime |
| title_full_unstemmed | Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime |
| title_short | Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime |
| title_sort | compactly supported stationary states of the degenerate keller segel system in the diffusion dominated regime |
| work_keys_str_mv | AT carrilloja compactlysupportedstationarystatesofthedegeneratekellersegelsysteminthediffusiondominatedregime AT sugiyamay compactlysupportedstationarystatesofthedegeneratekellersegelsysteminthediffusiondominatedregime |