Year: 2010
Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 1 : pp. 68–79
Abstract
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).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v23.n1.4
Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 1 : pp. 68–79
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Local gradient estimate
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