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arXiv · 1712.04024

A Differential Harnack Inequality for the Newell-Whitehead Equation

Derek Booth·Jack Burkart·Xiaodong Cao·Max Hallgren·Zachary Munro·Jason Snyder·Tom Stone
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Abstract

This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead equation on $\mathbb{R}^n$. We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation, including deriving a classical Harnack inequality, and characterizing standing solutions and traveling wave solutions.

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Derek Booth, Jack Burkart, Xiaodong Cao, Max Hallgren, Zachary Munro, Jason Snyder, Tom Stone. 2017-12-11. A Differential Harnack Inequality for the Newell-Whitehead Equation. https://arxiv.org/abs/1712.04024

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