@article{de Jong2025, 
author = {Thomas Geert de Jong and Georg Prokert and Alef Edou Sterk},
title = {Reaction–diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions},
year = {2025},
journal = {Networks and Heterogeneous Media},
volume = {20},
number = {1},
pages = {1-14},
keywords = {parabolic PDE, reaction–diffusion, diabetes, pancreas, asymptotic stability, gradient flow, monotone operator theory},
url = {https://www.sciopen.com/article/10.3934/nhm.2025001},
doi = {10.3934/nhm.2025001},
abstract = {We formulate and 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 the 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. Our results provide necessary theoretical steps for validation of the model.}
}