Differential Harnack inequality for a parabolic equation under the Finsler-geometric flow (Q2684821)

The authors obtain a global differential Harnack estimate for positive solutions of parabolic equation (1.2). In this paper, the authors consider Finsler-geometric flow equation (1.1), and they provided various gradient estimates for nonlinear heat equation (1.2) without the constraint condition on S-curvature. In particular they generalize them to the Finsler-Ricci flow, Finsler-Yamabe flow, and other geometric flows on compact Finsler manifolds. They also state and prove the Theorem (1.1) and Corollary (1.2) under global spacetime gradient for the Systems (1.1)--(1.4).