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Local Hamilton type Gradient Estimates and Harnack Inequalities for Nonlinear Parabolic Equations on Riemannian Manifolds

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Abstract

In this paper, we prove a local Hamilton type gradient estimate for positive solution of the nonlinear parabolic equation

$${u_t}(x,t) = \Delta u(x,t) + au(x,t)\ln \,u(x,t) + b{u^\alpha }(x,t),$$

on M × (−∞, ∞) with α ∈ R, where a and b are constants. As application, the Harnack inequalities are derived.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hefei Normal University, Hefei, 230601, China

    Wen Wang, Da-peng Xie & Hui Zhou

Authors
  1. Wen Wang
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  2. Da-peng Xie
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  3. Hui Zhou
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Correspondence to Wen Wang.

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The authors declare no conflict of interest.

Additional information

The project is supported by the National Natural Science Foundation of China (No. 12271039) and the Natural Science Foundation of universities of Anhui Province of China (Grant Nos. KJ2021A0927,2023AH040161).

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Wang, W., Xie, Dp. & Zhou, H. Local Hamilton type Gradient Estimates and Harnack Inequalities for Nonlinear Parabolic Equations on Riemannian Manifolds. Acta Math. Appl. Sin. Engl. Ser. 40, 539–546 (2024). https://doi.org/10.1007/s10255-024-1041-7

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  • DOI: https://doi.org/10.1007/s10255-024-1041-7

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