  This paper is focused on the generalized Forchheimer flows of slightly
compressible fluids in porous media. They are reformulated as a degenerate
parabolic equation for the pressure. The initial boundary value problem is
studied with time-dependent Dirichlet boundary data. The estimates up to the
boundary and for all time are derived for the $L^\infty$-norm of the pressure,
its gradient and time derivative. Large-time estimates are established to be
independent of the initial data. Particularly, thanks to the special structure
of the pressure's nonlinear equation, the global gradient estimates are
obtained in a relatively simple way, avoiding complicated calculations and a
prior requirement of H\"older estimates.
