Gradient estimates and Harnack inequalities for a Yamabe-type parabolic equation under the Yamabe flow

In this paper, we derive a series of gradient estimates and Harnack inequalities for positive solutions of a Yamabe-type parabolic partial differential equation (△-■t)u=pu+qu^(a+1) under the Yamabe flow. Here p,q∈C^(2,1)(M^(n)×[0,T]) and a is a positive constant.