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http://dx.doi.org/10.4134/JKMS.j190049

HARNACK ESTIMATES FOR NONLINEAR BACKWARD HEAT EQUATIONS WITH POTENTIALS ALONG THE RICCI-BOURGUIGNON FLOW  

Wang, Jian-Hong (School of Mathematical Sciences East China Normal University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 313-329 More about this Journal
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 [30]. The proof follows exactly the one given by X.-D. Cao [4] 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;
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