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April 10, 2024Open Access

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

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Abstract

We obtain almost optimal differential Harnack inequalities for a class of nonlinear parabolic equations on Riemannian manifolds with Bakry-\'{E}mery 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.

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Cite This Study

Zhihao Lu (2024) studied this question.

synapsesocial.com/papers/68e6fb90b6db643587675ebf https://doi.org/10.48550/arxiv.2404.06755

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