### Abstract

We consider a nonlocal analogue of the Fisher-KPP equation u_{t} = J * u - u + f(n), x ? R, f(0) = f(1) = 0, f > 0 on (0, 1), and its discrete counterpart u?_{n} = (J * u)_{n} - u _{n} + f(u_{n}), n ? Z, and show that travelling wave solutions of these equations that are bounded between 0 and 1 are unique up to translation. Our proof requires finding exact a priori asymptotics of a travelling wave. This we accomplish with the help of Ikehara's Theorem (which is a Tauberian theorem for Laplace transforms).

Original language | English |
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Pages (from-to) | 2433-2439 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 132 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2004 |

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## Cite this

Carr, J., & Chmaj, A. (2004). Uniqueness of travelling waves for nonlocal monostable equations.

*Proceedings of the American Mathematical Society*,*132*(8), 2433-2439. https://doi.org/10.1090/S0002-9939-04-07432-5