Hyperbolic Cauchy Problem Well Posed in the Class of Gevrey

  • Yujiro Ohya
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 52)


First of all, let us recall the two classical results of references [1] and [2]. These two papers are not related directly to the classical concept of hyperbolicity by J. Hadamard; that is, the well-posed Cauchy problem in the class of infinitely differentiable functions. Therefore, we were obliged to discuss the well-posedness in the class of Gevrey. In other words, we understand hyperbolicity when there is the influence (or dependence) domain extending the traditional hyperbolicity of differential operators.


Cauchy Problem Differential Operator Classical Concept Singular Integral Operator Partial Differential Operator 
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© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Yujiro Ohya
    • 1
  1. 1.University MomijigaokaTakarazuka HyogoJapan

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