## Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

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**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).## References

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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