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

11 Oct 2016 Dung Nguyen Thac Linh Kieu Thi Thuy Van Thu Ninh

In this paper, we consider the following general evolution equation $$u_t=\Delta_fu+au\log^\alpha u+bu$$ on smooth metric measure spaces $(M^n, g, e^{-f}dv)$. We give a local gradient estimate of Souplet-Zhang type for positive smooth solution of this equation provided that the Bakry-\'{E}mery curvature bounded from below... (read more)

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