For the Allen–Cahn equation, it is well known that there is a monotone standing wave joining 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 oscillations and they are obtained with the aid of variational arguments.
Traveling wave solutions to the Allen–Cahn equation / Chen, Chao-Nien; Coti Zelati, Vittorio. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 39:4(2022), pp. 905-926. [10.4171/aihpc/23]
Traveling wave solutions to the Allen–Cahn equation
Coti Zelati, Vittorio
2022
Abstract
For the Allen–Cahn equation, it is well known that there is a monotone standing wave joining 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 oscillations and they are obtained with the aid of variational arguments.File in questo prodotto:
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