On the filtration through porous media with partially soluble permeable grains

In this paper we consider the incompressible viscous fluid flow through a porous medium whose grains are also permeable and release mass to the flow. In each component porosity and permeability depend on saturation. The flow is modelled with a nonlinear parabolic equation for the pressure, with a degenerate parabolic term, depending not only on the saturations, but also on the space variable and on time averages of the saturation. We generalize the classic approach of Alt and Luckhaus to this situation and establish existence of at least one weak solution and bounds for its absolute value.