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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
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by Yunyan Yang PDF
Proc. Amer. Math. Soc. 136 (2008), 4095-4102 Request permission

Abstract:

Let $(M,g)$ be a complete noncompact Riemannian manifold. In this paper, we derive a local gradient estimate for positive solutions to a simple nonlinear parabolic equation \[ \frac {\partial u}{\partial t}=\Delta u+au\log u+bu\] on $M\times [0,+\infty )$, where $a$, $b$ are two real constants. This equation is closely related to the gradient Ricci soliton. We extend the result of L. Ma (Journal of Functional Analysis 241 (2006) 374-382).
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Additional Information
  • Yunyan Yang
  • Affiliation: Department of Mathematics, Information School, Renmin University of China, Beijing 100872, People’s Republic of China
  • Email: yunyanyang@ruc.edu.cn
  • Received by editor(s): April 19, 2007
  • Received by editor(s) in revised form: October 13, 2007
  • Published electronically: June 11, 2008
  • Additional Notes: The author was supported in part by the NSFC 10601065
  • Communicated by: Richard A. Wentworth
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 4095-4102
  • MSC (2000): Primary 58J05, 58J35
  • DOI: https://doi.org/10.1090/S0002-9939-08-09398-2
  • MathSciNet review: 2425752