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arXiv · 1505.07790

Gradient estimates of Hamilton - Souplet - Zhang type for a general heat equation on Riemannian manifolds

Nguyen Thac Dung·Nguyen Ngoc Khanh
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Abstract

The purpose of this paper is to study gradient estimate of Hamilton - Souplet - Zhang type for the general heat equation $$ u_t=\Delta_V u + au\log u+bu $$ on noncompact Riemannian manifolds. As its application, we show a Harnak inequality for the heat solution and a Liouville type theorem for a nonlinear elliptic equation. Our results are an extention and improvement of the work of Souplet - Zhang (\cite{SZ}), Ruan (\cite{Ruan}), Yi Li (\cite{Yili}) and Huang-Ma (\cite{HM}).

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BibTeXRIS

Nguyen Thac Dung, Nguyen Ngoc Khanh. 2015-05-28. Gradient estimates of Hamilton - Souplet - Zhang type for a general heat equation on Riemannian manifolds. https://arxiv.org/abs/1505.07790

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