| 书目名称 | Cauchy Problem for Differential Operators with Double Characteristics |
| 副标题 | Non-Effectively Hype |
| 编辑 | Tatsuo Nishitani |
| 视频video | |
| 概述 | Features thorough discussions on well/ill-posedness of the Cauchy problem for di?erential operators with double characteristics of non-e?ectively hyperbolic type.Takes a uni?ed approach combining geom |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | 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 |
| 出版日期 | Book 2017 |
| 关键词 | Cauchy problem; Well/ill-posedness; Non-effectively hyperbolic; IPH condition; Microlocal energy estimat |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-67612-8 |
| isbn_softcover | 978-3-319-67611-1 |
| isbn_ebook | 978-3-319-67612-8Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer International Publishing AG 2017 |
发表于 2025-3-21 17:27:10
