Displaying similar documents to “The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time”

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 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.