---

＜電子ブック＞
Cauchy Problem for Differential Operators with Double Characteristics : Non-Effectively Hyperbolic Characteristics / by Tatsuo Nishitani
(Lecture Notes in Mathematics. ISSN:16179692 ; 2202)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	VIII, 213 p. 7 illus : online resource
著者標目	*Nishitani, Tatsuo author SpringerLink (Online service)
件　名	LCSH:Differential equations FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-67612-8

 類似資料