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In this paper we prove some Hamilton type and Li-Yau type gradient estimateson positive solutions to generalized nonlinear parabolic equations on smoothmetric measure space with compact boundary. The geometry of the space in termsof lower bounds on the weighted Bakry-Emery Ricci curvature tensor and weightedmean curvature of the boundary are key in proving generalized local and globalgradient estimates. Various applications of these gradient estimates in termsof parabolic Harnack inequalities and Liouville type results are discussed.Further consequences to some specific models informed by the nature of thenonlinearities are highlighted.

Some gradient estimates for nonlinear heat-type equations on smooth metric measure spaces with compact boundary