Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics, Band 2202) - Softcover

Nishitani, Tatsuo

 
9783319676111: Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics, Band 2202)
Softcover
ISBN 10: 3319676113 ISBN 13: 9783319676111
Verlag: Springer, 2017

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Von der hinteren Coverseite

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 eigenvalues. 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 P µj , 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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2017
Sprache
Englisch
ISBN 10 
3319676113
ISBN 13 
9783319676111
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
224
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