Displaying similar documents to “Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators”

Cauchy problem in generalized Gevrey classes

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.

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

Nishitani, Tatsuo (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35L15, Secondary 35L30. In this paper we prove that for non effectively hyperbolic operators with smooth double characteristics with the Hamilton map exhibiting a Jordan block of size 4 on the double characteristic manifold the Cauchy problem is well posed in the Gevrey 6 class if the strict Ivrii-Petkov-Hörmander condition is satisfied.

The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable

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.