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arXiv · 2003.08248

Traveling wave solutions to the Allen-Cahn equation

Chao-Nien Chen·Vittorio Coti Zelati
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Abstract

For the Allen-Cahn equation, it is well known that there is a monotone standing wave joining with the balanced wells of the potential. In this paper we study the existence of traveling wave solutions for the Allen-Cahn equation on an infinite channel. Such traveling wave solutions possess a large number of oscillation and they are obtained with the aid of variational arguments.

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Chao-Nien Chen, Vittorio Coti Zelati. 2020-03-18. Traveling wave solutions to the Allen-Cahn equation. https://doi.org/10.4171/aihpc/23

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