Cauchy Problem for Differential Operators with Double Characteristics by Tatsuo Nishitani

Cauchy Problem for Differential Operators with Double Characteristics by Tatsuo Nishitani

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.

SKU	Unavailable
ISBN 13	9783319676111
ISBN 10	3319676113
Title	Cauchy Problem for Differential Operators with Double Characteristics
Author	Tatsuo Nishitani
Series	Lecture Notes In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer International Publishing AG
Year published	2017-11-26
Number of pages	213
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable