## 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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Pages (from-to) | 1791-1816 |

Number of pages | 26 |

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

Volume | 36 |

Issue number | 7 |

DOIs | |

Publication status | Published - Nov 1 2019 |

## Keywords

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

## ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Applied Mathematics