Biodegradation is a promising and efficient biological method for removing chemical pollutants in groundwater system due to its capability of utilizing native microorganisms under natural conditions. The process involves fluid flow and transport coupled to biological and chemical reactions. We consider a model system consisting of two reaction-diffusion-advection equations (for nutrient and pollutant concentrations) and a rate equation (for microbial population). The system admits both traveling fronts with constant speeds, and temporally oscillatory front solutions with time dependent speeds. To unveil the stability boundary in the parameter space, we take a hydrodynamic scaling limit, and derive reduced conservation laws which govern the limiting free boundary motion. The reduced equations help us find exact front solutions in several space dimensions and perform statistical analysis for heterogeneous advection velocities. An outline of future research problems comes at the end.
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