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An example of hyperbolic Cauchy problem not Gevrey well-posed for any lower order term

Le : 20/03/2009 13h30
Par : Tatsuo NISHITANI (Osaka University)
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Résumé : We give an example of second order hyperbolic operator for which the Cauchy problem is not Gevrey 6 well posed for any lower order term. This phenomenon is caused by the existence of a null bicharacteristic landing on the double characteristic manifold. Technically, this problem is closely related to the eigenvalue problems of complex Hamiltonian with cubic oscillator.