Titlebook: Cauchy Problem for Differential Operators with Double Characteristics; Non-Effectively Hype Tatsuo Nishitani Book 2017 Springer Internation

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Magda-Viola Hanke,Henryk Flachowskytangent bicharacteristics and no transition. In the last section we make some remarks on the Cauchy problem for . with transition of spectral type under the assumption of no tangent bicharacteristics.

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Tangent Bicharacteristics and Ill-Posedness,tangent bicharacteristics and no transition. In the last section we make some remarks on the Cauchy problem for . with transition of spectral type under the assumption of no tangent bicharacteristics.

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Non-effectively Hyperbolic Characteristics,prove that if . is of spectral type 1 on . then . always admits a local elementary factorization. On the other hand if . is of spectral type 2 even micolocal elementary factorization is not always possible. When . is of spectral type 2 near . we prove that . admits a “nice” microlocal factorization

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Microlocal Energy Estimates and Well-Posedness,proved microlocal energy estimates, the usual next procedure would be to obtain “local” energy estimates by partition of unity. Then one must get rid of the errors caused by the partition of unity. Sometimes it happens that the microlocal energy estimates is too weak to control such errors. In this

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