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

Year:    2019

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 2 : pp. 192–204

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.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-0005

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 2 : pp. 192–204

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Newell-Whitehead-Segel equation Harnack estimate Harnack inequality wave solutions.

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