A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation

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.