Traveling wave solutions of Allen–Cahn equation with a fractional Laplacian

Gui, Changfeng ; Zhao, Mingfeng

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 4, pp. 785-812.

Résumé

In this paper, we show the existence and qualitative properties of traveling wave solutions to the Allen–Cahn equation with fractional Laplacians. A key ingredient is the estimation of the traveling speed of traveling wave solutions.

Détail

DOI : 10.1016/j.anihpc.2014.03.005

Classification : 35B32, 35C07, 35J20, 35R09, 35R11, 45G05, 47G10
Keywords: Traveling wave solution, Traveling speed, Allen–Cahn equation, Fractional Laplacian, Continuation method, Hamiltonian identity

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