Abstract
In this chapter we provide a homogeneous second order differential operator P of spectral type 2 on Σ with polynomial coefficients with a bicharacteristic tangent to the double characteristic manifold and satisfies the Levi condition for which the Cauchy problem is ill-posed in the Gevrey class of order s > 5, in particular the Cauchy problem is C ∞ ill-posed . We also discuss some open questions on the Cauchy problem for P of spectral type 2 with tangent bicharacteristics and no transition. In the last section we make some remarks on the Cauchy problem for P with transition of spectral type under the assumption of no tangent bicharacteristics.
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Nishitani, T. (2017). Tangent Bicharacteristics and Ill-Posedness. In: Cauchy Problem for Differential Operators with Double Characteristics. Lecture Notes in Mathematics, vol 2202. Springer, Cham. https://doi.org/10.1007/978-3-319-67612-8_6
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DOI: https://doi.org/10.1007/978-3-319-67612-8_6
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