Hamilton-type gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive solution to a simple nonlinear parabolic equation

$ partial _t u = Delta u + aulog u + qu $ partial _t u = Delta u + aulog u + qu
Keywords:	Nonlinear parabolic equations   Li-Yau inequalities   Harnack differential inequalities   gradient estimates
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