Geodesic
Traveling wave solutions of Allen–Cahn equation with a fractional Laplacian
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 4, pp. 785-812

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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.

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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     author = {Gui, Changfeng and Zhao, Mingfeng},
     title = {Traveling wave solutions of {Allen{\textendash}Cahn} equation with a fractional {Laplacian}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {785--812},
     publisher = {Elsevier},
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Gui, Changfeng; Zhao, Mingfeng. Traveling wave solutions of Allen–Cahn equation with a fractional Laplacian. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 4, pp. 785-812. doi: 10.1016/j.anihpc.2014.03.005

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