Abstract
In this paper, we derive Li-Yau gradient estimates for the positive solution of a nonlinear parabolic equation \(u_{t}={\Delta } u -qu-au(\ln u)^{\alpha }\), where q is a C 2 function and a,α are constants, on a complete manifold (M,g) with bounded below Ricci curvature. The results generalize classical Li-Yau gradient estimates and some recent works on this direction.
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Zhu, X., Li, Y. Li-Yau Estimates for a Nonlinear Parabolic Equation on Manifolds. Math Phys Anal Geom 17, 273–288 (2014). https://doi.org/10.1007/s11040-014-9155-4
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DOI: https://doi.org/10.1007/s11040-014-9155-4