TY - JOUR
T1 - A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation
AU - Derek Booth, Jack Burkart, Xiaodong Cao, Max Hallgren, Zachary Munro, Jason Snyder & Tom Stone
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 - <p style="text-align: justify;">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&nbsp; characterizing standing solutions and traveling wave solutions.</p>