  We establish the existence of a solution to a non-linearly coupled
elliptic-parabolic system of PDEs describing the single-phase, miscible
displacement of one incompressible fluid by another in a porous medium. We
consider a velocity-dependent diffusion-dispersion tensor and model the action
of injection and production wells by measures on the domain. We obtain the
solution by passing to the limit on problems with regularised well data.
