@article {,
	title = {Gradient estimates of Hamilton{\textendash}Souplet{\textendash}Zhang type for a general heat equation on Riemannian manifolds},
	journal = {Archiv der Mathematik},
	volume = {105},
	year = {2015},
	pages = {479{\textendash}490},
	abstract = {<p>The purpose of this paper is to study gradient estimates of Hamilton{\textendash}Souplet{\textendash}Zhang type for the following general heat equation \$\$u\_t={\backslash}Delta\_V u + au{\backslash}log u+bu\$\$ u t = $Δ$ V u + a u log u + b u on noncompact Riemannian manifolds. As its application, we show a Harnack inequality for the positive solution and a Liouville type theorem for a nonlinear elliptic equation. Our results are an extension and improvement of the work of Souplet and Zhang (Bull London Math Soc 38:1045{\textendash}1053, 2006), Ruan (Bull London Math Soc 39:982{\textendash}988, 2007), Li (Nonlinear Anal 113:1{\textendash}32, 2015), Huang and Ma (Gradient estimates and Liouville type theorems for a nonlinear elliptic equation, Preprint, 2015), and Wu (Math Zeits 280:451{\textendash}468, 2015).</p>
},
	issn = {1420-8938},
	doi = {10.1007/s00013-015-0828-4},
	url = {http://dx.doi.org/10.1007/s00013-015-0828-4},
	author = {Dung, Nguyen Thac and Khanh, Nguyen Ngoc}
}
