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February 2015 Counterexamples to $C^{\infty}$ well posedness for some hyperbolic operators with triple characteristics
Enrico Bernardi, Tatsuo Nishitani
Proc. Japan Acad. Ser. A Math. Sci. 91(2): 19-24 (February 2015). DOI: 10.3792/pjaa.91.19


In this paper we prove a well posed and an ill posed result in the Gevrey category for a simple model hyperbolic operator with triple characteristics, when the principal symbol cannot be smoothly factorized, and whose propagation cone is not transversal to the triple characteristic manifold, thus confirming the conjecture that the Ivrii-Petkov condition is not sufficient for the $C^{\infty}$ well posedness unless the propagation cone is transversal to the characteristic manifold, albeit for a limited class of operators. Moreover we are able not only to disprove $C^{\infty}$ well posedness, but we can actually estimate the precise Gevrey threshold where well posedness will cease to hold.


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Enrico Bernardi. Tatsuo Nishitani. "Counterexamples to $C^{\infty}$ well posedness for some hyperbolic operators with triple characteristics." Proc. Japan Acad. Ser. A Math. Sci. 91 (2) 19 - 24, February 2015.


Published: February 2015
First available in Project Euclid: 2 February 2015

zbMATH: 1316.35170
MathSciNet: MR3310966
Digital Object Identifier: 10.3792/pjaa.91.19

Primary: 35L10

Keywords: Cauchy problem , Gevrey class , triple characteristics , well-posedness

Rights: Copyright © 2015 The Japan Academy

Vol.91 • No. 2 • February 2015
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