Investigating Processes for Pattern Creation using Coupled Bulk-Surface PDEs when Linear Reactions Occur

In this paper, the reaction-diffusion partial differential equations governing the coupled bulk surface in the presence of linear reactions are investigated. Suitable boundary conditions of linear Robin-type are imposed for the aforementioned system in both the bulk and on the surface on stationary volumes. The current situation is simulated using four PDE’s, namely, two equations for the bulk, and other two different equations are introduced for the surface bounding. The analyses methodology is depending on converting the system into dimensionless forms then rigorous linear stability analysis is performed to determine the necessary and sufficient conditions for pattern formation. Various cases are analyzed, namely, linear stability in the absence of diffusion and linear stability in the presence of diffusion. Furthermore, the necessary conditions for diffusion-driven instability for coupled system of bulk-surface reaction-diffusion equations (BSRDEs) are introduced together with the required wavenumbers.