GRADIENT ESTIMATES FOR A NONLINEAR HEAT EQUATION UNDER THE FINSLER-RICCI FLOW

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