Tangent Bicharacteristics and Ill-Posedness

  • Tatsuo Nishitani
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2202)

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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Tatsuo Nishitani
    • 1
  1. 1.Department of MathematicsOsaka UniversityToyonakaJapan

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