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<p>We obtain some almost optimal differential Harnack inequalities for a class of nonlinear parabolic equations on Riemannian manifolds with Bakry-Émery Ricci curvature bounded below, which includes the classical Fisher-KPP equation and Newell-Whitehead equation. Compared to existing research, we do not impose any additional conditions on the positive solutions. As its application, we derive some optimal Liouville properties.</p>

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Differential Harnack inequalities for Fisher-KPP type equations on Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Zhihao Lu

摘要

We obtain some almost optimal differential Harnack inequalities for a class of nonlinear parabolic equations on Riemannian manifolds with Bakry-Émery Ricci curvature bounded below, which includes the classical Fisher-KPP equation and Newell-Whitehead equation. Compared to existing research, we do not impose any additional conditions on the positive solutions. As its application, we derive some optimal Liouville properties.