### Abstract

We study entire solutions of a discrete diffusive equation with bistable nonlinearity. It is well known that there are three different wavefronts connecting any two of those three equilibria, say, 0, a, 1. We construct three different types of entire solutions. The first one is a solution which behaves as two opposite wavefronts (connecting 0 and 1) of the same positive speed approaching each other from both sides of the real line. The second one is a solution which behaves as two different wavefronts (connecting a and one of {0, 1}) approaching each other from both sides of the real line and converging to the wavefront connecting 0 and 1. The third one is a solution which behaves as a wavefront connecting a and 0 and a wavefront connecting 0 and 1 approaching each other from both sides of the real line.

Original language | English |
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Pages (from-to) | 450-458 |

Number of pages | 9 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 347 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Nov 15 |

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### Keywords

- Asymptotic behavior
- Discrete diffusive equation
- Entire solution
- Wavefront

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics