  In this paper we study the porous medium equation (PME) coupled with the
Ricci flow on complete manifolds with bounded nonnegative curvature operator.
In particular, we derive Aronson-B\'enilan and Li-Yau-Hamilton type
differential Harnack estimates for positive solutions to the PME, with a linear
forcing term, under the Ricci flow.

Differential Geometry;Analysis of PDEs