Cauchy problem for differential operators with double characteristics : non-effectively hyperbolic characteristics / Tatsuo Nishitani.

Include index and bibliographical references and index.

1. Introduction.-
2 Non-effectively hyperbolic characteristics.-
3 Geometry of bicharacteristics.-
4 Microlocal energy estimates and well-posedness.-
5 Cauchy problemâ no tangent bicharacteristics. -
6 Tangent bicharacteristics and ill-posedness.-
7 Cauchy problem in the Gevrey classes.-
8 Ill-posed Cauchy problem, revisited.-
References.

Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for differential operators with non-effectively hyperbolic double characteristics. Previously scattered over numerous different publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well/ill-posedness of the Cauchy problem.