Cauchy Problem for Differential Operators with Double Characteristics (Paperback)

Tatsuo Nishitani

ISBN 10: 3319676113 / ISBN 13: 9783319676111

Edité par Springer International Publishing AG, Cham, 2017

Paperback. Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for dierential operators with non-eectively hyperbolic double characteristics. Previously scattered over numerous dierent 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 dierential operator P of order m (i.e. one where Pm = dPm = 0) is eectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is eectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms.If there is a non-eectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between Puj and Puj, where iuj 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 insucient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9783319676111

Synopsis :

Features thorough discussions on well/ill-posedness of the Cauchy problem for differential operators with double characteristics of non-effectively hyperbolic type

Takes a unified approach combining geometrical and microlocal tools

Adopts the viewpoint that the Hamilton map and the geometry of bicharacteristics characterizes the well/ill-posedness of the Cauchy problem

Détails bibliographiques

Titre : Cauchy Problem for Differential Operators ...
Éditeur : Springer International Publishing AG, Cham
Date d'édition : 2017
Reliure : Paperback
Etat : new
Edition : Edition originale