TY - JOUR T1 - A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation JO - Analysis in Theory and Applications VL - 2 SP - 192 EP - 204 PY - 2019 DA - 2019/04 SN - 35 DO - http://doi.org/10.4208/ata.OA-0005 UR - https://global-sci.org/intro/article_detail/ata/13113.html KW - Newell-Whitehead-Segel equation, Harnack estimate, Harnack inequality, wave solutions. AB -

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.