Global weak solutions to a fractional Cahn-Hilliard cross-diffusion system in lymphangiogenesis
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916353354498048 |
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| author | Jüngel, Ansgar Li, Yue |
| author_facet | Jüngel, Ansgar Li, Yue |
| contents | A spectral-fractional Cahn-Hilliard cross-diffusion system, which describes the pre-patterning of lymphatic vessel morphology in collagen gels, is studied. The model consists of two higher-order quasilinear parabolic equations and describes the evolution of the fiber phase volume fraction and the solute concentration. The free energy consists of the nonconvex Flory-Huggins energy and a fractional gradient energy, modeling nonlocal long-range correlations. The existence of global weak solutions to this system in a bounded domain with no-flux boundary conditions is shown. The proof is based on a three-level approximation scheme, spectral-fractional calculus, and a priori estimates coming from the energy inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global weak solutions to a fractional Cahn-Hilliard cross-diffusion system in lymphangiogenesis Jüngel, Ansgar Li, Yue Analysis of PDEs 35D30, 35K35, 35K65, 35K67, 92C37 A spectral-fractional Cahn-Hilliard cross-diffusion system, which describes the pre-patterning of lymphatic vessel morphology in collagen gels, is studied. The model consists of two higher-order quasilinear parabolic equations and describes the evolution of the fiber phase volume fraction and the solute concentration. The free energy consists of the nonconvex Flory-Huggins energy and a fractional gradient energy, modeling nonlocal long-range correlations. The existence of global weak solutions to this system in a bounded domain with no-flux boundary conditions is shown. The proof is based on a three-level approximation scheme, spectral-fractional calculus, and a priori estimates coming from the energy inequality. |
| title | Global weak solutions to a fractional Cahn-Hilliard cross-diffusion system in lymphangiogenesis |
| topic | Analysis of PDEs 35D30, 35K35, 35K65, 35K67, 92C37 |
| url | https://arxiv.org/abs/2408.05972 |