@Article{JPDE-23-68,
author = {},
title = {Gradient Estimates for a Nonlinear Diffusion Equation on Complete Manifolds},
journal = {Journal of Partial Differential Equations},
year = {2010},
volume = {23},
number = {1},
pages = {68--79},
abstract = {<p>Let (M,g) be a complete non-compact Riemannian manifold with the m- dimensional Bakry-Émery Ricci curvature bounded below by a non-positive constant. In this paper, we give a localized Hamilton-type gradient estimate for the positive smooth bounded solutions to the following nonlinear diffusion equation u_t=Δu-∇φ·∇u-au\log u-bu, where φ is a C^2 function, and a ≠ 0 and b are two real constants. This work generalizes the results of Souplet and Zhang (Bull. London Math. Soc., 38 (2006), pp. 1045-1053) and Wu (Preprint, 2008).</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v23.n1.4},
url = {http://global-sci.org/intro/article_detail/jpde/5222.html}
}