  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.
