| |  Online-Ressource |
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| Verfasst von: | Nishitani, Tatsuo  |
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| Titel: | Cauchy Problem for Differential Operators with Double Characteristics |
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| Titelzusatz: | Non-Effectively Hyperbolic Characteristics |
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| Verf.angabe: | by Tatsuo Nishitani |
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| Verlagsort: | Cham |
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| Verlag: | Springer |
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| Jahr: | 2017 |
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| Umfang: | Online-Ressource (VIII, 213 p. 7 illus, online resource) |
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| Gesamttitel/Reihe: | Lecture Notes in Mathematics ; 2202 |
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| | SpringerLink : Bücher |
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| ISBN: | 978-3-319-67612-8 |
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| Abstract: | 1. Introduction -- 2 Non-effectively hyperbolic characteristics.- 3 Geometry of bicharacteristics.- 4 Microlocal energy estimates and well-posedness.- 5 Cauchy problem−no tangent bicharacteristics. - 6 Tangent bicharacteristics and ill-posedness.- 7 Cauchy problem in the Gevrey classes.- 8 Ill-posed Cauchy problem, revisited -- References |
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| | 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. A doubly characteristic point of a differential operator P of order m (i.e. one where Pm = dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigenvalues. When the characteristics are at most double and every double characteristic is effectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between − Pµj and P µj , where iµj are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 × 4 Jordan block, the spectral structure of FPm is insufficient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role |
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| DOI: | doi:10.1007/978-3-319-67612-8 |
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| URL: | Resolving-System: https://doi.org/10.1007/978-3-319-67612-8 |
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| | Volltext: http://dx.doi.org/10.1007/978-3-319-67612-8 |
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| | Cover: https://swbplus.bsz-bw.de/bsz495983004cov.jpg |
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| | Inhaltstext: https://zbmath.org/?q=an:1400.35001 |
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| | DOI: https://doi.org/10.1007/978-3-319-67612-8 |
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| Schlagwörter: | (s)Cauchy-Anfangswertproblem / (s)Differentialoperator |
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| | (s)Cauchy-Anfangswertproblem |
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| Datenträger: | Online-Ressource |
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| Sprache: | eng |
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| Bibliogr. Hinweis: | Erscheint auch als : Druck-Ausgabe: Nishitani, Tatsuo: Cauchy problem for differential operators with double characteristics. - Cham : Springer Nature, 2017. - viii, 211 Seiten |
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| RVK-Notation: | SI 850 |
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| Sach-SW: | Differential equations |
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| | Mathematics |
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| | Partial differential equations |
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| K10plus-PPN: | 1657203603 |
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| Verknüpfungen: | → Übergeordnete Aufnahme |
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| Lokale URL UB: |  Zum Volltext |
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978-3-319-67612-8
Cauchy Problem for Differential Operators with Double Characteristics / Nishitani, Tatsuo; 2017 (Online-Ressource)
68197126
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