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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 69, Issue 2


Gradient estimates for a nonlinear heat equation under the Finsler-Ricci flow

Fanqi Zeng / Qun He
Published Online: 2019-03-19 | DOI: https://doi.org/10.1515/ms-2017-0233


This paper considers a compact Finsler manifold (Mn, F(t), m) evolving under the Finsler-Ricci flow and establishes global gradient estimates for positive solutions of the following nonlinear heat equation: tu=Δmu,

where Δm is the Finsler-Laplacian. As applications, several Harnack inequalities are obtained.

MSC 2010: Primary 35K55; Secondary 53C21

Keywords: gradient estimate; nonlinear heat equation; Harnack inequality; Akbarzadeh’s Ricci tensor; Finsler-Ricci flow


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About the article

This work was supported by NNSFC (Nos. 11471246, 11671361) and Nanhu Scholars Program for Young Scholars of XYNU.

Received: 2017-09-30

Accepted: 2018-03-29

Published Online: 2019-03-19

Published in Print: 2019-04-24

(Communicated by Július Korbaš)

Citation Information: Mathematica Slovaca, Volume 69, Issue 2, Pages 409–424, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0233.

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