Global existence and numerical simulations of a coupled two-cell activator-inhibitor reaction-diffusion system

R. Douaifia, S. Abdelmalek

A coupled two-cell Brusselator system subject to Neumann boundary conditions is considered. Firstly, we obtain the global existence of classical solutions for the system. Then, with the aim of showing the model dynamics, we develop a positivity preserving splitting technique to find the numerical solution of the proposed model. The numerical scheme leads to the convergence of the solution to a steady-state or to the equilibrium point. 

Tbilisi Mathematical Journal, Special Issue (8 - 2021), pp. 39-49