Coherent and focusing multidimensional nonlinear geometric optics
J.-L. Joly, G. Métivier, J. Rauch (1995)
Annales scientifiques de l'École Normale Supérieure
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J.-L. Joly, G. Métivier, J. Rauch (1995)
Annales scientifiques de l'École Normale Supérieure
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Nicolas Burq, Patrick Gérard, Nikolay Tzvetkov (2005)
Annales scientifiques de l'École Normale Supérieure
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Pierre Degond (1986)
Annales scientifiques de l'École Normale Supérieure
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Ferruccio Colombini, Daniele del Santo, Tamotu Kinoshita (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.
F. Colombini, E. Jannelli, S. Spagnolo (1983)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Kunihiko Kajitani, Yasuo Yuzawa (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We discuss the local existence and uniqueness of solutions of certain nonstrictly hyperbolic systems, with Hölder continuous coefficients with respect to time variable. We reduce the nonstrictly hyperbolic systems to the parabolic ones and by use of the and the Banach scale method we construct a semi-group which gives a representation of the solution to the Cauchy problem.