## Abstract

We are concerned with classical solutions to the initial value problem for u = |u|^{p} or u = |ut|^{p} in R^{n} x [0, ∞) with "small" data. If the data have compact support, it is partially known that there is a critical number p0(n) such that most solutions blow-up in finite time for 1 < p ≤ p0(n) and a global solution exists for p > p0(n). In this paper, we shall show for all n ≥ 2 that, if the support of data is noncompact, there are blowing-up solutions even for p > p0(n) because of the "bad" spatial decay of the initial data. Moreover, critical decays for each equation are conjectured. The proof lies in the pointwise estimates of the fundamental solution of.

Original language | English |
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Pages (from-to) | 647-661 |

Number of pages | 15 |

Journal | Differential and Integral Equations |

Volume | 8 |

Issue number | 3 |

Publication status | Published - 1995 Jan 1 |

Externally published | Yes |

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics