Harnack estimates for nonlinear backward heat equations with potentials along the Ricci-Bourguignon flow
J. Korean Math. Soc. 2020 Vol. 57, No. 2, 313-329
https://doi.org/10.4134/JKMS.j190049
Published online March 1, 2020
Jian-Hong Wang
East China Normal University
Abstract : In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu \cite{[WJY12]}. The proof follows exactly the one given by X.-D. Cao \cite{[CXD08]} for the linear backward heat type equations coupled with the Ricci flow.
Keywords : Harnack estimate, nonlinear backward heat type equation, Ricci-Bourguignon flow, blow up
MSC numbers : 53C44
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