On a nonlinear parabolic system modelling miscible compressible displacement in porous media

We give an existence result for a nonlinear parabolic system modelling the single-phase miscible displacement of one slightly compressible fluid by another in a porous medium. To this aim, we study the asymptotic behaviour of a flow at low dispersion coefficients. We use suitable test functions to establish a priori estimates, and then compactness arguments to pass to the limit in a perturbated problem. We also state the existence and the uniqueness of a strong solution.