Blow-up for semilinear wave equations with slowly decaying data in high dimensions

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14 Citations (Scopus)

Abstract

We are concerned with classical solutions to the initial value problem for u = |u|p or u = |ut|p in Rn 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 languageEnglish
Pages (from-to)647-661
Number of pages15
JournalDifferential and Integral Equations
Volume8
Issue number3
Publication statusPublished - 1995 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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