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| Artikel-Nr.: 858A-9783319676111 Herst.-Nr.: 9783319676111 EAN/GTIN: 9783319676111 |
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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 eigen values. 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 Pµj, 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. Weitere Informationen: | | Author: | Tatsuo Nishitani | Verlag: | Springer International Publishing | Sprache: | eng |
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| Weitere Suchbegriffe: Differenzialgleichung / Gewöhnliche, Gewöhnliche Differenzialgleichung, Differenzialgleichung / Partielle, Partielle Differenzialgleichung, Cauchy problem, Well/ill-posedness, Non-effectively hyperbolic, IPH condition, Microlocal energy estimates, Tangent bicharacteristic, Gevrey classes |
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