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On the existence in Gevrey classes of local solutions to the Cauchy problem for nonlinear hyperbolic systems with Hölder continuous coefficients

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Abstract

In this paper we shall solve locally in time the solutions to the Cauchy problem for first order quasilinear hyperbolic systems of which coefficients of principal part and of lower order terms are μ- Hölder and \(\mu'\)- Hölder continuous in time variable respectively and in Gevrey class of index s with respect to space variables under the assumption \(1\le s <\min\{1 + \frac\mu \nu,1+\frac{1-\mu+\mu'}{\nu}\}, 0<\mu\le1\), where ν denotes the maximal muliplicity of characteristics of systems.

Keywords: Nonlinear hyperbolic systems, Cauchy problem, Gevrey classes

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Authors and Affiliations

  1. Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

    Kunihiko Kajitani

  2. Center for Tsukuba Advanced Research Alliance, University of Tsukuba, Tennoudai 1-1-1, Tsukuba city, Ibaraki 315-8577, Japan

    Yasuo Yuzawa

Authors
  1. Kunihiko Kajitani
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  2. Yasuo Yuzawa
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Kajitani, K., Yuzawa, Y. On the existence in Gevrey classes of local solutions to the Cauchy problem for nonlinear hyperbolic systems with Hölder continuous coefficients. Ann. Univ. Ferrara 52, 303–315 (2006). https://doi.org/10.1007/s11565-006-0023-4

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  • DOI: https://doi.org/10.1007/s11565-006-0023-4

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