@Article{JPDE-33-17,
author = {Zeng , Fanqi},
title = {Gradient Estimates for a Nonlinear Heat Equation Under Finsler-Geometric Flow},
journal = {Journal of Partial Differential Equations},
year = {2020},
volume = {33},
number = {1},
pages = {17--38},
abstract = {<p style="text-align: justify;">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 <br/>$$\partial_{t}u(x,t)=\Delta_{m} u(x,t),~~~~~~~~~~(x,t)\in M\times[0,T],$$</p><p style="text-align: justify;">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.&nbsp; Finally, we give an application to the 
Finsler-Yamabe flow.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v33.n1.2},
url = {http://global-sci.org/intro/article_detail/jpde/15801.html}
}