English

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

Analysis of PDEs 2025-09-04 v1 Cell Behavior

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.

Keywords

Cite

@article{arxiv.2305.03397,
  title  = {Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions},
  author = {T. G. de Jong and G. Prokert and A. E. Sterk},
  journal= {arXiv preprint arXiv:2305.03397},
  year   = {2025}
}