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arXiv · 2608.20590

A Differential Harnack Inequality for the FitzHugh-Nagumo Equation

Xiaodong Cao·Harry Fluck·Sophia Teng
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Abstract

In this paper we develop a Li-Yau-Hamilton (LYH) type differential Harnack estimate for positive solutions to the FitzHugh-Nagumo equation on $\mathbb{R}^n$. We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation, including a classical Harnack inequality and a lower bound for the speed of traveling wave solutions.

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Xiaodong Cao, Harry Fluck, Sophia Teng. 2026-08-20. A Differential Harnack Inequality for the FitzHugh-Nagumo Equation. https://arxiv.org/abs/2608.20590

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