A Hamilton-Souplet-Zhang type gradient estimate for a class of parabolic equations on Finsler manifolds

Abstract

Employing a new Laplacian comparison theorem, we have derived a Souplet-Zhang type gradient estimate for a specific nonlinear parabolic equation (Finslerian logarithmic Schrödinger equation) on a non-compact forward complete Finsler manifold with some curvatures bounded from below. All the coefficients in our equations vary with time on the manifold. As applications, we obtain a local Harnack inequality and a Liouville-type theorem.