Synthèse
Volume 30, Numéro 2, Pages 38-44
2025-12-01
Analysis And Simulations Of Bulk-surface Reaction-diffusion Systems
Authors : Madzvamuse Anotida .
Abstract
In this work, we study a coupled bulk-surface reaction-diffusion system defined on a stationary domain, where the dynamics in the bulk are linked to those on the surface through mixed Robin-type boundary conditions. These conditions represent a nonlinear exchange of molecular species between the bulk and the surface, relevant to applications in cell and developmental biology, as well as ecological models involving interacting populations.We derive general conditions for diffusion-driven instability in this coupled setting, extending the classical Turing criteria to bulk-surface systems. These conditions allow us to predict the onset of pattern formation depending on the diffusion coefficients in the bulk and on the surface—whether patterns arise in the bulk, on the surface, or in both regions.Our theoretical results are supported by numerical simulations using the bulk-surface finite element method, employing piecewise bilinear basis functions for spatial discretization and a fractional-step q-scheme for time integration.
Keywords
bulk-surface reaction-diffusion system
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