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

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.

References in corpus (6)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Weak SINDy For Partial Differential Equations
• Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems
• Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks
• Pattern Formation in a Coupled Membrane-Bulk Reaction-Diffusion Model for Intracellular Polarization and Oscillations
• Fungal tip growth arising through a codimension-1 global bifurcation