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Cauchy Problem for Differential Operators with Double Characteristics

Non-Effectively Hyperbolic Characteristics

Produktform: Buch / Einband - flex.(Paperback)

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.weiterlesen

Dieser Artikel gehört zu den folgenden Serien

Sprache(n): Englisch

ISBN: 978-3-319-67611-1 / 978-3319676111 / 9783319676111

Verlag: Springer International Publishing

Erscheinungsdatum: 26.11.2017

Seiten: 213

Auflage: 1

Autor(en): Tatsuo Nishitani

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