DIFFERENTIAL HARNACK ESTIMATES FOR POROUS MEDIUM EQUATIONS UNDER GEOMETRIC FLOWS
HONGJUAN LI *
Department of Mathematics, Henan Normal University, Xinxiang 453007, P. R. China
BINGQING MA
Department of Mathematics, Henan Normal University, Xinxiang 453007, P. R. China
*Author to whom correspondence should be addressed.
Abstract
In this paper, we study the porous medium equation coupled with general geometric flows. We obtain Aronson-Bernilan and Li-Yau-Hamilton type differential estimates for positive solutions to the porous medium equations, which generalize the recent work of Cao and Zhu in [1].
Keywords: Harnack estimates, geometric flows, porous medium equations