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

Abstract

Abstract 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: ∂ t u = Δ m u , $$\begin{array}{} \partial_{t}u=\Delta_{m} u, \end{array} $$ where Δ m is the Finsler-Laplacian. As applications, several Harnack inequalities are obtained.