(untitled) (Journal of Partial Differential Equations, 2020)
"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_tu(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.00a0 Finally, we give an application to the Finsler-Yamabe flow."