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

Thomas Geert de Jong*, Georg Prokert, Alef Edou Sterk

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We formulate and 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 the 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. Our results provide necessary theoretical steps for validation of the model.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalNetworks and Heterogeneous Media
Volume20
Issue number1
DOIs
Publication statusPublished - 2025

Keywords

  • asymptotic stability
  • diabetes
  • gradient flowmonotone operator theory
  • pancreas
  • parabolic PDE
  • reaction–diffusion

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