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arXiv · 2305.03397

Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions

T. G. de Jong·G. Prokert·A. E. Sterk
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Abstract

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.

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T. G. de Jong, G. Prokert, A. E. Sterk. 2023-05-05. Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions. https://doi.org/10.3934/nhm.2025001

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