Critical Curve for p-q Systems of Nonlinear Wave Equations in Three Space Dimensions

Rentaro Agemi, Yuki Kurokawa, Hiroyuki Takamura

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)

Abstract

The existence of the critical curve for p-q systems for nonlinear wave equations was already established by D. Del Santo, V. Georgiev, and E. Mitidieri [1997, Global existence of the solutions and formation of singularities for a class of hyperbolic systems, in "Geometric Optics and Related Topics" (F. Colombini and N. Lerner, Eds.), Progress in Nonlinear Differential Equations and Their Applications, Vol. 32, pp. 117-139, Birkhäuser, Basel] except for the critical case. Our main purpose is to prove a blow-up theorem for which the nonlinearity (p, q) is just on the critical curve in three space dimensions. Moreover, the lower and upper bounds of the lifespan of solutions are precisely estimated, including the sub-critical case.

Original languageEnglish
Pages (from-to)87-133
Number of pages47
JournalJournal of Differential Equations
Volume167
Issue number1
DOIs
Publication statusPublished - 2000 Oct 10
Externally publishedYes

Keywords

  • Nonlinear wave equations; three space dimension; lifespan

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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