株式会社極東書店トップ ＞ 商品一覧 ＞ Cauchy Problem for Differential Operators with Double Characteristics : Non-Effectively Hyperbolic Characteristics. 1st ed. 2017.
商品詳細
Cauchy Problem for Differential Operators with Double Characteristics : Non-Effectively Hyperbolic Characteristics. 1st ed. 2017.
・ISBN 978-3-319-67611-1 paper EUR 49.99
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| 著者・編者 | Nishitani, Tatsuo, |
|---|---|
| シリーズ | Lecture Notes in Mathematics |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2017 |
| ページ数 | 213 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-4780＞ |
解説
Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for di?erential operators with non-e?ectively hyperbolic double characteristics. Previously scattered over numerous di?erent 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 di?erential operator P of order m (i.e. one where Pm = dPm = 0) is e?ectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is e?ectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms.
If there is a non-e?ectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between ?P?j and P?j, where i?j are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 x 4 Jordan block, the spectral structure of FPm is insu?cient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.
A doubly characteristic point of a di?erential operator P of order m (i.e. one where Pm = dPm = 0) is e?ectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is e?ectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms.
If there is a non-e?ectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between ?P?j and P?j, where i?j are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 x 4 Jordan block, the spectral structure of FPm is insu?cient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.