Scaling up of source terms with random behavior for modelling transport migration of contaminants in aquifers

We are interested in studying the evolution in time of the concentration of a pollutant which is transported by diffusion and convection from a “source site” made of a large number of similar “local sources”. Assuming the release curve (source emission vs. space and time), of each local source, being random, our aim is to give a mathematical model describing the global evolution of such a system and numerical simulations illustrating the theoretical results.