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Harnack estimate for a semilinear parabolic equation

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Abstract

We study the Cauchy problem of a semilinear parabolic equation. We construct an appropriate Harnack quantity and get a differential Harnack inequality. Using this inequality, we prove the finite-time blowup of the positive solutions and recover a classical Harnack inequality. We also obtain a result of Liouville type for the elliptic equation.

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Authors and Affiliations

  1. Department of Applied Mathematics, College of Science, China Agricultural University, Beijing, 100083, China

    SongBo Hou & Liang Zou

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  1. SongBo Hou
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  2. Liang Zou
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Correspondence to SongBo Hou.

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Hou, S., Zou, L. Harnack estimate for a semilinear parabolic equation. Sci. China Math. 60, 833–840 (2017). https://doi.org/10.1007/s11425-016-0270-6

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  • DOI: https://doi.org/10.1007/s11425-016-0270-6

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