### Abstract

We investigate the asymptotic behavior of weak solutions to the semilinear non autonomous wave equation u_{tt} - Δu + u_{t}|u_{t}|^{p-1} = V(t)u|u|^{p-1} + f(.,t), where V(t) is a positive time dependent potential satisfying V(t) = O((1 + t)^{-λ}) as t → +∞ and f_{t} decays to 0 as t → +∞. We show that for 0 ≤ λ ≤ p there are initial values such that the energy norm of the corresponding solutions grows at least polynomially as t → +∞, while if λ > p the energy norm remains uniformly bounded for any choice of initial values; moreover, in certain cases there is an absorbing ball for the orbits.

Original language | English |
---|---|

Pages (from-to) | 53-68 |

Number of pages | 16 |

Journal | Nonlinear Differential Equations and Applications |

Volume | 5 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics