Cauchy Problem for Differential Operators with Double Characteristics

Non-Effectively Hyperbolic Characteristics

Autor: Tatsuo Nishitani

Jazyk:

Vazba: Brožovaná

Vydavatel: Springer International Publishing AG

Dostupnost: Skladem u dodavatele

Odesíláme za 5-8 dnů

1 147 Kč

Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-po...

Informace o knize

Autor

Tatsuo Nishitani

Jazyk

Angličtina

Vazba

Kniha - Brožovaná

Vydáno

2017

Stránek

213

EAN

9783319676111

ISBN

3319676113

Enbook ID

17963706

Vydavatel

Springer International Publishing AG

Hmotnost

352

Rozměry

233 x 154 x 19

Kompletní popis

Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for di erential operators with non-e ectively hyperbolic double characteristics. Previously scattered over numerous di erent 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 di erential operator P of order m (i.e. one where Pm = dPm = 0) is e ectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is e ectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-e ectively 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 insu cient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.

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Cauchy Problem for Differential Operators with Double Characteristics

Non-Effectively Hyperbolic Characteristics

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