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 Perelman type entropy formulae and differential Harnack estimates for weighted doubly nonlinear diffusion equations under curvature dimension condition Bull. Korean Math. Soc. 2021 Vol. 58, No. 6, 1539-1561 https://doi.org/10.4134/BKMS.b210087Published online November 8, 2021Printed November 30, 2021 Yu-Zhao Wang Shanxi University Abstract : We prove Perelman type $\mathcal{W}$-entropy formulae and differential Harnack estimates for positive solutions to weighed doubly nonlinear diffusion equation on weighted Riemannian manifolds with $CD(-K,m)$ condition for some $K\ge0$ and $m\ge n$, which are also new for the non-weighted case. As applications, we derive some Harnack inequalities. Keywords : Weighted doubly nonlinear diffusion equations, Perelman type entropy formula, differential Harnack estimates, Bakry-\'Emery Ricci curvature, curvature dimension condition. MSC numbers : Primary 58J35, 35K92, 35K55 Supported by : This work was financially supported by NSFC No. 11701347. Downloads: Full-text PDF   Full-text HTML

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