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On the Global Behavior of Classical Solutions to Coupled Systems of Semilinear Wave Equations

  • Hideo Kubo
  • Masahito Ohta
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 159)

Abstract

The aim of this work is twofold. One is to develop an approach for dealing with semilinear wave equations adopted by John [38]. In Section 2, the basis of the argument will be explained in a self-contained way. The other is an application of the approach to systems of wave equations. We shall make use of it to handle the semilinear case in Sections 3,4 and 5, and to consider the quasilinear case in Section 6. In these argument we bring such systems that the single wave components obey different propagation speeds into focus.

Keywords

Nonlinear hyperbolic systems global solutions blow-up lifespan self-similar solutions asymptotic behavior 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Hideo Kubo
    • 1
  • Masahito Ohta
    • 2
  1. 1.Department of Mathematics, Graduate School of ScienceOsaka UniversityOsaka ToyonakaJapan
  2. 2.Department of Mathematics, Faculty of ScienceSaitama UniversitySaitamaJapan

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