Local Aronson-Bénilan gradient estimates and Harnack inequality for the porous medium equation along Ricci flow
Local Aronson-Bénilan gradient estimates and Harnack inequality for the porous medium equation along Ricci flow
In this paper, we prove some new local Aronson-Bénilan type gradient estimates for positive solutions of the porous medium equation $u_{t}=Δ u^{m}, m>1$ coupled with Ricci flow, assuming that the Ricci curvature is bounded. As application, the related Harnack inequality is derived. Our results generalize known results. These results may …