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Some Necessary Conditions for Hyperbolic Systems

  • Tatsuo Nishitani
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 46)

Abstract

In this article some necessary conditions in order for the Cauchy problem for hyperbolic systems to be well posed will be studied. In the scalar case, from Ivrii-Petkov [1], for the well-posedness of the Cauchy problem, a set of vanishing conditions on the lower order terms must be verified at a multiple characteristic. Our purpose is to find some necessary conditions which correspond to the Ivrii-Petkov conditions for systems. In [2], we obtained a necessary condition in this direction. Here we continue this study.

Keywords

Cauchy Problem Differential Operator Asymptotic Solution Hyperbolic System Scalar Case 
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References

  1. [1]
    V.Ja. Ivrii and V.M. Petkov, Necessary conditions for the Cauchy problem for nonstrictly hyperbolic equations to be well posed, Uspehi Mat.Nauka, 29 (1974), 3–70.Google Scholar
  2. [2]
    A. Bove and T. Nishitani, Necessary conditions for the well posedness of the Cauchy problem for hyperbolic systems, preprint, 1999.Google Scholar
  3. [3]
    T. Nishitani, Strongly hyperbolic systems of maximal rank, Publ. RIMS Kyoto. Univ., 33 (1997), 765–773.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Tatsuo Nishitani
    • 1
  1. 1.Department of MathematicsOsaka UniversityToyonaka OsakaJapan

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