Year: 2020
Author: Fanqi Zeng
Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 1 : pp. 17–38
Abstract
This paper considers a compact Finsler manifold $(M^n, F(t), m)$
evolving under a Finsler-geometric flow and establishes global gradient
estimates for positive solutions of the following nonlinear heat
equation
$$\partial_{t}u(x,t)=\Delta_{m} u(x,t),~~~~~~~~~~(x,t)\in M\times[0,T],$$
where $\Delta_{m}$ is the Finsler-Laplacian. By integrating the gradient estimates, we derive the corresponding Harnack inequalities. Our results generalize and correct the work of S. Lakzian, who established similar results for the Finsler-Ricci flow. Our results are also natural extension of similar results on Riemannian-geometric flow, previously studied by J. Sun. Finally, we give an application to the Finsler-Yamabe flow.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v33.n1.2
Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 1 : pp. 17–38
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Gradient estimate nonlinear heat equation Harnack inequality Akbarzadeh's Ricci tensor Finsler-geometric flow.
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