On a Coupled Reaction Diffusion System with Time Delays

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Abstract
In a two-compartment model for cellular control by repression there arises a coupled system of reaction diffusion equations which governs the densities of the chemical species in the compartments. The reaction mechanism in this model is affected by time delays and the coupling of the equations is through the interface of the two compartments. The purpose of this paper is to give a qualitative analysis of this unusual coupled reaction diffusion system with time delays. This analysis includes the existence and uniqueness of a global time-dependent solution and the corresponding steady state solution, iterative methods for the construction of the solution, and local and global stability of the steady-state solution. Also included is the uniform boundedness of the solution.