Analysis of a filtration model in porous media

We prove the existence of wave front solutions to a system of partial differential equations that models the transport and accretion of suspended particles in porous media. The model includes a variable porosity that depends on the volume of immobile particles retained through filtration. We also examine an initial boundary value problem associated with these equations and use singular perturbation to obtain an approximation in the case the particle concentration is small. A local existence theorem of the leading order approximation completes the work.