Gradient Estimate For A Nonlinear Parabolic Equation Under Geometric Flow

This thesis is a study on the theory of local gradient estimates for positive solutions of a nonlinear parabolic equation on Riemannian manifold under general geometric flow.In this paper,through the Li-Yau gradient estimate and Jun Sun's research on the gradient estimate of heat equation under general geometric flow,we will derive local first-and second-order gradient estimates for positive solutions of a nonlinear parabolic equation on Riemannian manifold under general geometric flow.These results can be regarded as a generlization of the results of Wang et al.At the same time,we give a corresponding Harnack inequality.