Anal. Theory Appl., 35 (2019), pp. 192-204.
Published online: 2019-04
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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.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0005}, url = {http://global-sci.org/intro/article_detail/ata/13113.html} }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.