Volume 35, Issue 2
A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation

Derek Booth ,  Jack Burkart ,  Xiaodong Cao ,  Max Hallgren ,  Zachary Munro and Jason Snyder & Tom Stone

10.4208/ata.OA-0005

Anal. Theory Appl., 35 (2019), pp. 192-204.

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  • Abstract

This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead-Segel 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.

  • AMS Subject Headings

35C07, 35K10, 35K55

Published online: 2019-04