  In this paper we prove that weak solutions to the Diffusive Wave
Approximation of the Shallow Water equations $$ \partial_t u - \nabla\cdot
((u-z)^\alpha|\nabla u|^{\gamma-1}\nabla u) = f $$ are locally bounded. Here,
$u$ describes the height of the water, $z$ is a given function that represents
the land elevation and $f$ is a source term accounting for evaporation,
infiltration or rainfall.
