A mathematical model for bioremediation processes of polluted soils.

Bioremediation of soils exploits selected species of bacteria able to metabolize a specific pollutant (typically a hydrocarbon). Bacteria are injected and proliferate creating a biofilm over the soil scheleton where they feed on the pollutant. We consider in particular the case in which bacteria are transported by an unsaturated flow, which, despite its importance, has not been treated extensively in the literature. The mathematical problem consists of a system of coupled nonlinear partial differential equations for which an existence theorem is proved using a technique of nested fixed points.