A Differential Harnack Inequality for the Newell-Whitehead Equation

11 Dec 2017  ·  Booth Derek, Burkart Jack, Cao Xiaodong, Hallgren Max, Munro Zachary, Snyder Jason, Stone Tom ·

This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead 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...

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Analysis of PDEs