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

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 [...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 57; no. 2; pp. 313 - 329
Main Author Wang, Jian-Hong
Format Journal Article
LanguageKorean
Published 2020
Subjects
Ricci-Bourguignon flow
blow up
nonlinear backward heat type equation
Harnack estimate
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Summary: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.
Bibliography:KISTI1.1003/JNL.JAKO202012941165925
ISSN:0304-9914