  We study the generalized Forchheimer flows of slightly compressible fluids in
heterogeneous porous media. The media's porosity and coefficients of the
Forchheimer equation are functions of the spatial variables. The partial
differential equation for the pressure is degenerate in its gradient and can be
both singular and degenerate in the spatial variables. Suitable weighted
Lebesgue norms for the pressure, its gradient and time derivative are
estimated. The continuous dependence on the initial and boundary data is
established for the pressure and its gradient with respect to those
corresponding norms. Asymptotic estimates are derived even for unbounded
boundary data as time tends to infinity.
