### Abstract

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.

Original language | English |
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Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Keywords

- Asymmetric
- Balanced
- Reaction-diffusion equation
- Traveling front

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Applied Mathematics