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}
}