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Volume 35, Issue 2
A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation

Derek Booth, Jack Burkart, Xiaodong Cao, Max Hallgren, Zachary Munro, Jason Snyder & Tom Stone

DOI: 10.4208/ata.OA-0005

Anal. Theory Appl., 35 (2019), pp. 192-204.

Published online: 2019-04

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Newell-Whitehead-Segel equation, Harnack estimate, Harnack inequality, wave solutions.

  • AMS Subject Headings

35C07, 35K10, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-35-192, author = {Derek Booth, Jack Burkart, Xiaodong Cao, Max Hallgren, Zachary Munro, Jason Snyder and Tom Stone}, title = {A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation}, journal = {Analysis in Theory and Applications}, year = {2019}, volume = {35}, number = {2}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0005}, url = {http://global-sci.org/intro/article_detail/ata/13113.html} }
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 -

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.

Derek Booth, Jack Burkart, Xiaodong Cao, Max Hallgren, Zachary Munro, Jason Snyder and Tom Stone. (2019). A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation. Analysis in Theory and Applications. 35 (2). 192-204. doi:10.4208/ata.OA-0005
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