  This paper concerns a space-time homogenization limit of nonnegative weak
solutions to porous medium equations. In particular, the so-called homogenized
matrix will be characterized in terms of solutions to cell problems, which
drastically vary in a scaling parameter $r > 0$. A similar problem has already
been studied in [1], where the growth of the power nonlinearity is strictly
restricted due to some substantial obstacles. In the present paper, such
obstacles will be overcome by developing local uniform estimates for the
gradients of nonnegative weak solutions.
