Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions
T. G. de Jong, G. Prokert, A. E. Sterk
Published: 2023/5/5
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.