Gradient estimates and Harnack inequalities for Yamabe-type parabolic equations on Riemannian manifolds

Let (M-n, g) be a complete noncompact n-dimensional Riemannian manifolds. In this paper, we consider the following Yamabe-type parabolic equation u(t) = Delta u + au + bu(alpha) on M-n x [0, infinity). We give a global gradient estimate of Hamilton-type for positive smooth solutions of this equation provided that Ricci curvature bounded from below. As its application, we show a dimension-free Harnack inequality and a Liouville-type theorem for nonlinear elliptic equations. (C) 2018 Elsevier B.V. All rights reserved.