In this paper, we consider the gradient estimates for the positive solutions to the following porous medium equation
$u_t = \Delta_V u^m$,
where $m>1$. We obtain Li-Yau type bounds of the above equation on Riemannian manifolds with Bakry-Emery type curvature bounded from below, which improves the estimates in  and covers the ones in [22, 18, 19, 27].
"Gradient estimates of a general porous medium equation for the V-Laplacian." Kodai Math. J. 43 (1) 16 - 41, March 2020. https://doi.org/10.2996/kmj/1584345686