Journal
MATHEMATICA SLOVACA
Volume 69, Issue 2, Pages 409-424Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/ms-2017-0233
Keywords
gradient estimate; nonlinear heat equation; Harnack inequality; Akbarzadeh's Ricci tensor; Finsler-Ricci flow
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Funding
- NNSFC [11471246, 11671361]
- Nanhu Scholars Program for Young Scholars of XYNU
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This paper considers a compact Finsler manifold (M-n; F(t);m) evolving under the Finsler-Ricci flow and establishes global gradient estimates for positive solutions of the following non-linear heat equation: partial derivative(t)u = Delta(m)u, where Delta(m) is the Finsler-Laplacian. As applications, several Harnack inequalities are obtained. (C) 2019 Mathematical Institute Slovak Academy of Sciences
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