An elementary proof of the exponential blow‐up for semi‐linear wave equations

研究成果: Article査読

16 被引用数 (Scopus)

抄録

This paper deals with the upper bound of the life span of classical solutions to □u = ∣u∣p, u∣t = 0 = εφ(x), utt=0 = εψ(x) with the critical power of p in two or three space dimensions. Zhou has proved that the rate of the upper bound of this life span is exp(ε−p(p−1)). But his proof, especially the two‐dimensional case, requires many properties of special functions. Here we shall give simple proofs in each space dimension which are produced by pointwise estimates of the fundamental solution of □. We claim that both proofs are done in almost the same way.

本文言語English
ページ(範囲)239-249
ページ数11
ジャーナルMathematical Methods in the Applied Sciences
17
4
DOI
出版ステータスPublished - 1994 4月 10
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)
  • 工学(全般)

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