$\mathcal{W}$-Entropy formulae and differential Harnack estimates for porous medium equations on Riemannian manifolds

Abstract

In this paper, we prove Perelman type $\mathcal{W}$-entropy formulae and global differential Harnack estimates for positive solutions to porous medium equation on the closed Riemannian manifolds with Ricci curvature bounded below. As applications, we derive Harnack inequalities and Laplacian estimates.