On Existence and Uniqueness Results for a Coupled System Modeling Miscible Displacement in Porous Media

Initial boundary value problems for a nonlinear differential system of two equations are considered in this paper. This system of equations, one of elliptic form for the pressure and the other of parabolic form for the concentration of one fluid, governs the miscible displacement of one incompressible fluid by another in a porous medium. Under some reasonable assumptions on the data, it is proved that the system possesses a weak solution, and uniqueness is also established for the semiclassical solution of the system.