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

Let (Mn,g) be a complete noncompact n-dimensional Riemannian manifolds. In this paper, we consider the following Yamabe-type parabolic equationut=Δu+au+buα on Mn×[0,∞). 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.