On reaction-diffusion equations derived from a PEPA model

This work presents an extension of the fluid approximation to the diffusion approximation for a PEPA model. The diffusion approximation leads to a reaction-diffusion system in which the spatial or location information is considered, while it is ignored in the fluid approximation approach. The fundamental results for the solution of the reaction-diffusion equations, such as the existence, uniqueness, positivity and convergence, have been established. Numerical simulations are also given to illustrate the analytical results. (C) 2011 Elsevier Ltd. All rights reserved.