Displaying similar documents to “Cauchy problem in generalized Gevrey classes”

Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators

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...

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.

On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem

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.