Gradient estimates for some evolution equations on complete smooth metric measure spaces

Nguyen Thac Dung, Kieu Thi Thuy Linh, Ninh Van Thu

In this paper, we consider the following general evolution equation $$u_t={\Delta }_{f}u+au{\log }^{\alpha }u+bu$$ on smooth metric measure spaces $(M^n,g,e^{-f}dv)$. We give a local gradient estim…