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- W2895535502 abstract "In this paper, we prove sharp gradient estimates for a positive solution to the heat equation $u_t=Delta u+aulog u$ in complete noncompact Riemannian manifolds. As its application, we show that if $u$ is a positive solution of the equation $u_t=Delta u$ and $log u$ is of sublinear growth in both spatial and time directions then $u$ must be constant. This gradient estimate is sharp since it is well-known that $u(x,t)=e^{x+t}$ satisfying $u_t=Delta u$. We also emphasize that our results are better than those given by Jiang (cite{XJ16}), Souplet-Zhang (cite{SZ06}), Wu (cite{Wu15, Wu17}), and others." @default.
- W2895535502 created "2018-10-12" @default.
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- W2895535502 date "2018-10-07" @default.
- W2895535502 modified "2023-09-23" @default.
- W2895535502 title "Sharp gradient estimates for a heat equation in Riemannian manifolds" @default.
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- W2895535502 hasPublicationYear "2018" @default.
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