The lifespan of solutions to nonlinear systems of a high-dimensional wave equation

Vladimir Georgiev*, Hiroyuki Takamura, Zhou Yi

*この研究の対応する著者

研究成果: Article査読

20 被引用数 (Scopus)

抄録

In this work we study the lifespan of solutions to a p-q system in the higher-dimensional case n≥4. A suitable local existence curve in the p-q plane is found. The curve characterizes the local solutions in Sobolev space Hs with s≥0. Further, some lower and upper bounds of the lifespan of classical solutions are found too. This work is an extension of work [Geometric Optics and Related Topics, Progress in Nonlinear Differential Equations and their Applications, vol. 32, Birkhäuser, Basel, 1997, pp. 117-140], where a suitable global existence small data curve is studied. In the subcritical case, we give almost precise results for the lower bounds of the lifespan by using a suitable weighted Strichartz estimate for the higher-dimensional wave equation.

本文言語English
ページ(範囲)2215-2250
ページ数36
ジャーナルNonlinear Analysis, Theory, Methods and Applications
64
10
DOI
出版ステータスPublished - 2006 5 15
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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