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The Mixed Problem for Hyperbolic Systems

  • Seiichiro Wakabayashi
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 65)

Abstract

Lax [27] and Mizohata [34] proved that for the non-characteristic Cauchy problem to be C well-posed it is necessary that the characteristic roots are real. In the mixed problem Kajitani [23] obtained the results corresponding to those in the Cauchy problem under some restrictive assumptions. In §3 we shall relax his assumptions (see, also, [52]). We note that well-posedness of the mixed problems has been investigated by many authors ([1], [2], [19], [20], [22], [26], [32], [33], [38]). We shall consider the mixed problem for hyperbolic systems with constant coefficients in a quarter-space in §§4–6. Hersh [13], [l4], [15] studied the mixed problem for hyperbolic systems with constant coefficients. He gave the necessary and sufficient condition for the mixed problem to be C well-posed. However, his proof seems to be incomplete (see [25]). Sakamoto [37] justified his results for single higher order hyperbolic equations (see, also, [40], [41] [42]). In §4 we shall consider C well-posedness of the mixed problem. Duff [11] studied the location and structures of singularities of the fundamental solutions of the mixed problems for single higher order hyperbolic equations, using the stationary phase method.

Keywords

Cauchy Problem Fundamental Solution Constant Coefficient Hyperbolic System Hyperbolic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Seiichiro Wakabayashi
    • 1
  1. 1.Institute of Mathematicsthe University of TsukubaIbarakiJapan

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