In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear heat equations. Firstly, we derive such an estimate on a Kahler manifold with a fixed Kahler metric. Then we consider the estimate on Kahler manifolds with Kahler metrics evolving under the rescaled Kahler-Ricci flow. Both of the estimates are generalized to constrained cases. Finally, we extend the estimtes to more general nonlinear heat equations on both Riemannian manifolds and Kahler manifolds.
机构:Jiangsu Ocean Univ, Sch Sci, Lianyungang 222005, Peoples R China
Liu, Hao-Yue
Yao, Sha
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Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Peoples R ChinaJiangsu Ocean Univ, Sch Sci, Lianyungang 222005, Peoples R China
Yao, Sha
Ren, Xin-An
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Jiangsu Ocean Univ, Sch Sci, Lianyungang 222005, Peoples R China
China Univ Min & Technol, Sch Math, Xuzhou 221116, Peoples R ChinaJiangsu Ocean Univ, Sch Sci, Lianyungang 222005, Peoples R China
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Harbin Normal Univ, Sch Math Sci, Harbin 150025, Heilongjiang, Peoples R ChinaHarbin Normal Univ, Sch Math Sci, Harbin 150025, Heilongjiang, Peoples R China
Shi, Shujun
Zhang, Wei
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Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R ChinaHarbin Normal Univ, Sch Math Sci, Harbin 150025, Heilongjiang, Peoples R China