Underground pollution: Some solutions of the transport equation

The diffusion of a soluble compound in a porous medium is ruled by convection, molecular diffusion, and mechanical dispersion. Liquid motion, thermal agitation, and mixing phenomenon are responsible of the compound dynamic behavior. In this paper, the transport phenomenon and the general governing equation were considered. After finding symmetries of the model in the monodimensional case, we found wide classes of invariant solutions. Finally, we found the exact solution concerning with a realistic engineering problem.