Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 7, pp. 1791-1816.
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For a balanced bistable reaction-diffusion equation, an axisymmetric traveling front has been well known. This paper proves that an axially asymmetric traveling front with any positive speed does exist in a balanced bistable reaction-diffusion equation. Our method is as follows. We use a pyramidal traveling front for an unbalanced reaction-diffusion equation whose cross section has a major axis and a minor axis. Preserving the ratio of the major axis and a minor axis to be a constant and taking the balanced limit, we obtain a traveling front in a balanced bistable reaction-diffusion equation. This traveling front is monotone decreasing with respect to the traveling axis, and its cross section is a compact set with a major axis and a minor axis when the constant ratio is not 1.

DOI : 10.1016/j.anihpc.2019.05.001
Classification : 35C07, 35B20, 35K57
Mots-clés : Traveling front, Reaction-diffusion equation, Asymmetric, Balanced 
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     title = {Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Taniguchi, Masaharu. Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 7, pp. 1791-1816. doi : 10.1016/j.anihpc.2019.05.001. http://www.numdam.org/articles/10.1016/j.anihpc.2019.05.001/

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