Overview
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.
The book, Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics #2202) [Bulk, Wholesale, Quantity] ISBN#9783319676111 in Paperback by Tatsuo Nishitani may be ordered in bulk quantities. Minimum starts at 25 copies. Availability based on publisher status and quantity being ordered.
Details
Format:
Paperback
Publication Date:
11/26/2017
ISBN-13:
9783319676111
Pages:
213
Publisher:
Springer International Publishing
