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.
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Annales de l'Institut Henri Poincaré C, Analyse non linéaire
© 2019 Elsevier Masson SAS. All rights reserved.
|Web of Science KeyUT|
Masaharu Taniguchi, Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 36, Issue 7, 2019, Pages 1791-1816, ISSN 0294-1449, https://doi.org/10.1016/j.anihpc.2019.05.001.
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|Open Archive (publisher)||