Li-Yau-Hamilton Estimates For Nonlinear Parabolic Equations

In this paper,study the Li-Yau-Hamilton estimates for positive solutions of nonlinear parabolic equations on a complete Riemannian manifold.I first study the Li-Yau-Hamilton estimate for a positive solution to the equation(?f-q-(?))u=au(ln u)? with Bakry-Emery-Ricci curvature bounded from below.Secondly,I obtain the similar estimate for a positive solution to the equation(?q(t)-q-(?))u=au(ln u)?,where(M,g(t))t?[0,T]is a complete solution to the Ricci flow(?)g(t)=-ZRicg(t).