  This article is devoted to the study of several estimations for a positive
solution to a nonlinear weighted parabolic equation on a weighted Riemannian
manifold. We therefore derive new Li-Yau type and Hamilton type gradient
estimates yielding several consequences. We also derive Hessian estimate and
some corollaries for the same equation. Among the applications of our estimates
discussed here are Harnack type inequalities, Liouville type theorems and a
local time reversed Harnack inequality.
