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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.
We study the simplest system of partial differential equations: that is, two equations of first order partial differential equation with two independent variables with real analytic coefficients. We describe a necessary and sufficient condition for the Cauchy problem to the system to be C infinity well posed. The condition will be expressed by inclusion relations of the Newton polygons of some scalar functions attached to the system. In particular, we can give a characterization of the strongly...
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