Pressure jump and radial stationary solutions of the degenerate Cahn–Hilliard equation
The Cahn–Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues, following the theory of mixtures. We are interested in quantifying the pressure jump at the interface between phases in the case of incompressible flows. To do so, we depart from th...
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Académie des sciences
2023-05-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.173/ |
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| author | Elbar, Charles Perthame, Benoît Skrzeczkowski, Jakub |
| author_facet | Elbar, Charles Perthame, Benoît Skrzeczkowski, Jakub |
| author_sort | Elbar, Charles |
| collection | DOAJ |
| description | The Cahn–Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues, following the theory of mixtures. We are interested in quantifying the pressure jump at the interface between phases in the case of incompressible flows. To do so, we depart from the spherically symmetric dynamical compressible model and include an external force. We prove existence of stationary states as limits of the parabolic problems. Then we prove the incompressible limit and characterize compactly supported stationary solutions. This allows us to compute the pressure jump in the small dispersion regime and in particular the force dependent curvature effect. |
| format | Article |
| id | doaj-art-edb80b4e2fe04df6be427b9ddf4ce66e |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-edb80b4e2fe04df6be427b9ddf4ce66e2025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-05-01351S137539410.5802/crmeca.17310.5802/crmeca.173Pressure jump and radial stationary solutions of the degenerate Cahn–Hilliard equationElbar, Charles0Perthame, Benoît1Skrzeczkowski, Jakub2Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions, F-75005 Paris, FranceSorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions, F-75005 Paris, FranceFaculty of Mathematics, Informatics and Mechanics, University of Warsaw, Stefana Banacha 2, 02-097 Warsaw, PolandThe Cahn–Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues, following the theory of mixtures. We are interested in quantifying the pressure jump at the interface between phases in the case of incompressible flows. To do so, we depart from the spherically symmetric dynamical compressible model and include an external force. We prove existence of stationary states as limits of the parabolic problems. Then we prove the incompressible limit and characterize compactly supported stationary solutions. This allows us to compute the pressure jump in the small dispersion regime and in particular the force dependent curvature effect.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.173/Degenerate Cahn–Hilliard equationAsymptotic AnalysisIncompressible limitHele–Shaw equationsSurface tensionPressure jump |
| spellingShingle | Elbar, Charles Perthame, Benoît Skrzeczkowski, Jakub Pressure jump and radial stationary solutions of the degenerate Cahn–Hilliard equation Comptes Rendus. Mécanique Degenerate Cahn–Hilliard equation Asymptotic Analysis Incompressible limit Hele–Shaw equations Surface tension Pressure jump |
| title | Pressure jump and radial stationary solutions of the degenerate Cahn–Hilliard equation |
| title_full | Pressure jump and radial stationary solutions of the degenerate Cahn–Hilliard equation |
| title_fullStr | Pressure jump and radial stationary solutions of the degenerate Cahn–Hilliard equation |
| title_full_unstemmed | Pressure jump and radial stationary solutions of the degenerate Cahn–Hilliard equation |
| title_short | Pressure jump and radial stationary solutions of the degenerate Cahn–Hilliard equation |
| title_sort | pressure jump and radial stationary solutions of the degenerate cahn hilliard equation |
| topic | Degenerate Cahn–Hilliard equation Asymptotic Analysis Incompressible limit Hele–Shaw equations Surface tension Pressure jump |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.173/ |
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