### Abstract

We derive a precise decay estimate of the solutions to the Cauchy problem for the Klein-Gordon equation with a nonlinear dissipation: [formula] where ρ(x, t, v) is a function like ρ = a(x)(1 + t)^{θ}|v|^{r}v, − 1 < r, with a(x) ≥ 0 supported on Ω_{R} = (x ∈ R^{N}||x| ≥ R) for some R > 0.

Original language | English |
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Pages (from-to) | 245-271 |

Number of pages | 27 |

Journal | Hokkaido Mathematical Journal |

Volume | 27 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

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### Keywords

- Decay
- Localized dissipation
- Wave equation

### ASJC Scopus subject areas

- Mathematics(all)