Competing effects in fourth‐order aggregation–diffusion equations
We give sharp conditions for global in time existence of gradient flow solutions to a Cahn–Hilliard‐type equation, with backwards second‐order degenerate diffusion, in any dimension and for general initial data. Our equation is the 2‐Wasserstein gradient flow of a free energy with two competing effe...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Wiley
2024
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| _version_ | 1811140340077297664 |
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| author | Antonio Carrillo, J Esposito, A Falcó, C Fernández‐Jiménez, A |
| author_facet | Antonio Carrillo, J Esposito, A Falcó, C Fernández‐Jiménez, A |
| author_sort | Antonio Carrillo, J |
| collection | OXFORD |
| description | We give sharp conditions for global in time existence of gradient flow solutions to a Cahn–Hilliard‐type equation, with backwards second‐order degenerate diffusion, in any dimension and for general initial data. Our equation is the 2‐Wasserstein gradient flow of a free energy with two competing effects: the Dirichlet energy and the power‐law internal energy. Homogeneity of the functionals reveals critical regimes that we analyse. Sharp conditions for global in time solutions, constructed via the minimising movement scheme, also known as JKO scheme, are obtained. Furthermore, we study a system of two Cahn–Hilliard‐type equations exhibiting an analogous gradient flow structure. |
| first_indexed | 2024-09-25T04:20:25Z |
| format | Journal article |
| id | oxford-uuid:5e15ac91-51e2-49e9-9c9b-5058806ea4ab |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:20:25Z |
| publishDate | 2024 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:5e15ac91-51e2-49e9-9c9b-5058806ea4ab2024-08-01T19:33:42ZCompeting effects in fourth‐order aggregation–diffusion equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5e15ac91-51e2-49e9-9c9b-5058806ea4abEnglishJisc Publications RouterWiley2024Antonio Carrillo, JEsposito, AFalcó, CFernández‐Jiménez, AWe give sharp conditions for global in time existence of gradient flow solutions to a Cahn–Hilliard‐type equation, with backwards second‐order degenerate diffusion, in any dimension and for general initial data. Our equation is the 2‐Wasserstein gradient flow of a free energy with two competing effects: the Dirichlet energy and the power‐law internal energy. Homogeneity of the functionals reveals critical regimes that we analyse. Sharp conditions for global in time solutions, constructed via the minimising movement scheme, also known as JKO scheme, are obtained. Furthermore, we study a system of two Cahn–Hilliard‐type equations exhibiting an analogous gradient flow structure. |
| spellingShingle | Antonio Carrillo, J Esposito, A Falcó, C Fernández‐Jiménez, A Competing effects in fourth‐order aggregation–diffusion equations |
| title | Competing effects in fourth‐order aggregation–diffusion equations |
| title_full | Competing effects in fourth‐order aggregation–diffusion equations |
| title_fullStr | Competing effects in fourth‐order aggregation–diffusion equations |
| title_full_unstemmed | Competing effects in fourth‐order aggregation–diffusion equations |
| title_short | Competing effects in fourth‐order aggregation–diffusion equations |
| title_sort | competing effects in fourth order aggregation diffusion equations |
| work_keys_str_mv | AT antoniocarrilloj competingeffectsinfourthorderaggregationdiffusionequations AT espositoa competingeffectsinfourthorderaggregationdiffusionequations AT falcoc competingeffectsinfourthorderaggregationdiffusionequations AT fernandezjimeneza competingeffectsinfourthorderaggregationdiffusionequations |