Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908515797303296 |
|---|---|
| author | de Jong, T. G. Prokert, G. Sterk, A. E. |
| author_facet | de Jong, T. G. Prokert, G. Sterk, A. E. |
| contents | We investigate a nonlinear parabolic reaction-diffusion equation describing the oxygen concentration in encapsulated pancreatic cells with a general core-shell geometry. This geometry introduces a discontinuous diffusion coefficient as the material properties of the core and shell differ. We apply monotone operator theory to show well-posedness of the problem in the strong form. Furthermore, the stationary solutions are unique and asymptotically stable. These results rely on the gradient structure of the underlying PDE. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03397 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions de Jong, T. G. Prokert, G. Sterk, A. E. Analysis of PDEs Cell Behavior 92C50, 35K55, 34K20 We investigate a nonlinear parabolic reaction-diffusion equation describing the oxygen concentration in encapsulated pancreatic cells with a general core-shell geometry. This geometry introduces a discontinuous diffusion coefficient as the material properties of the core and shell differ. We apply monotone operator theory to show well-posedness of the problem in the strong form. Furthermore, the stationary solutions are unique and asymptotically stable. These results rely on the gradient structure of the underlying PDE. |
| title | Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions |
| topic | Analysis of PDEs Cell Behavior 92C50, 35K55, 34K20 |
| url | https://arxiv.org/abs/2305.03397 |