Cauchy Problem for Differential Operators with Double Characteristics is popular PDF and ePub book, written by Tatsuo Nishitani in 2017-11-24, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Cauchy Problem for Differential Operators with Double Characteristics can be Read Online from any device for your convenience.
Cauchy Problem for Differential Operators with Double Characteristics Book PDF Summary
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.
Detail Book of Cauchy Problem for Differential Operators with Double Characteristics PDF
- Author : Tatsuo Nishitani
- Release : 24 November 2017
- Publisher : Springer
- ISBN : 9783319676128
- Genre : Mathematics
- Total Page : 215 pages
- Language : English
- PDF File Size : 21,7 Mb
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