### Abstract

This paper is concerned with the Cauchy problem for the semilinear wave equation: u_{tt} -δu = F(u) in ℝn × [0,∞); where the space dimension n ≥2, F(u) = |u|^{p} or F(u) = |u|^{p-1}u with p > 1. Here, the Cauchy data are non-zero and non-compactly supported. Our results on the blow-up of positive radial solutions (not necessarily radial in low dimensions n = 2; 3) generalize and extend the results of Takamura [19] for zero initial position and Takamura, Uesaka and Wakasa [21] for zero initial velocity. The main technical difficulty in the paper lies in obtaining the lower bounds for the free solution when both initial position and initial velocity are non-identically zero in even space dimensions.

Original language | English |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Differential and Integral Equations |

Volume | 29 |

Issue number | 1-2 |

Publication status | Published - 2016 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

*Differential and Integral Equations*,

*29*(1-2), 1-18.