Cauchy problem for hyperbolic systems in Gevrey class. A note on Gevrey indices
Hideo Yamahara (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Hideo Yamahara (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Daniela Calvo (2003)
Banach Center Publications
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In this work we present a class of partial differential operators with constant coefficients, called multi-quasi-hyperbolic and defined in terms of a complete polyhedron. For them we obtain the well-posedness of the Cauchy problem in generalized Gevrey classes determined by means of the same polyhedron. We present some necessary and sufficient conditions on the operator in order to be multi-quasi-hyperbolic and give some examples.
H. Komatsu (1980-1981)
Séminaire Équations aux dérivées partielles (Polytechnique)
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N. Iwasaki (1985-1986)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Daniela Calvo (2006)
Bollettino dell'Unione Matematica Italiana
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We prove the well-posedness of the Cauchy Problem for first order weakly hyperbolic systems in the multi-anisotropic Gevrey classes, that generalize the standard Gevrey spaces. The result is obtained under the following hypotheses: the principal part is weakly hyperbolic with constant coefficients, the lower order terms satisfy some Levi-type conditions; and lastly the coefficients of the lower order terms belong to a suitable anisotropic Gevrey class. In the proof it is used the quasi-symmetrization...
Bernardi, Enrico, Bove, Antonio (2008)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 34E20, 35L80, 35L15. In this paper we study an ODE in the complex plane. This is a key step in the search of new necessary conditions for the well posedness of the Cauchy Problem for hyperbolic operators with double characteristics.
Milena Petrini (1995)
Rendiconti del Seminario Matematico della Università di Padova
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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.
Massimo Cicognani (1991)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Tatsuo Nishitani (1998)
Journées équations aux dérivées partielles
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We study the simplest system of partial differential equations: that is, two equations of first order partial differential equation with two independent variables with real analytic coefficients. We describe a necessary and sufficient condition for the Cauchy problem to the system to be C infinity well posed. The condition will be expressed by inclusion relations of the Newton polygons of some scalar functions attached to the system. In particular, we can give a characterization of the...