Well-posedness results for general reaction-diffusion transport of oxygen in encapsulated cells
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917712661315584 |
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| author | Nakamura, Yuma Putri, Kharisma Surya Sterk, Alef de Jong, Thomas Geert |
| author_facet | Nakamura, Yuma Putri, Kharisma Surya Sterk, Alef de Jong, Thomas Geert |
| contents | In this paper, we provide well-posedness results for nonlinear parabolic PDEs given by reaction-diffusion equations describing the concentration of oxygen in encapsulated cells. The cells are described in terms of a core and a shell, which introduces a discontinuous diffusion coefficient as the material properties of the core and shell differ. In addition, the cells are subject to general nonlinear consumption of oxygen. As no monotonicity condition is imposed on the consumption monotone operator theory cannot be used. Moreover, the discontinuity in the diffusion coefficient bars us to apply classical results. However, by directly applying a Galerkin method we obtain uniqueness and existence of the strong form solution. These results will provide the basis to study the dynamics of cells in critical states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness results for general reaction-diffusion transport of oxygen in encapsulated cells Nakamura, Yuma Putri, Kharisma Surya Sterk, Alef de Jong, Thomas Geert Analysis of PDEs 35K57, 35K55 In this paper, we provide well-posedness results for nonlinear parabolic PDEs given by reaction-diffusion equations describing the concentration of oxygen in encapsulated cells. The cells are described in terms of a core and a shell, which introduces a discontinuous diffusion coefficient as the material properties of the core and shell differ. In addition, the cells are subject to general nonlinear consumption of oxygen. As no monotonicity condition is imposed on the consumption monotone operator theory cannot be used. Moreover, the discontinuity in the diffusion coefficient bars us to apply classical results. However, by directly applying a Galerkin method we obtain uniqueness and existence of the strong form solution. These results will provide the basis to study the dynamics of cells in critical states. |
| title | Well-posedness results for general reaction-diffusion transport of oxygen in encapsulated cells |
| topic | Analysis of PDEs 35K57, 35K55 |
| url | https://arxiv.org/abs/2401.09863 |