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Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics: 2202 (Lecture Notes in Mathematics) - Tapa blanda
Sinopsis
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.
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De la contraportada
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 eigenvalues. 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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Cham, Springer, 2017
ISBN 10: 3319676113
ISBN 13: 9783319676111
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Cauchy Problem for Differential Operators with Double Characteristics. Non-Effectively Hyperbolic Characteristics.
Publicado por
Cham, Springer., 2017
ISBN 10: 3319676113
ISBN 13: 9783319676111
Antiguo o usado
Tapa blanda
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Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics)
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Cauchy Problem for Differential Operators With Double Characteristics : Non-effectively Hyperbolic Characteristics
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Cauchy Problem for Differential Operators With Double Characteristics : Non-effectively Hyperbolic Characteristics
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Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics)
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Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics, 2202)
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Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics)
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Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics, 2202)
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Cauchy Problem for Differential Operators with Double Characteristics (Paperback)
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Springer International Publishing AG, Cham, 2017
ISBN 10: 3319676113
ISBN 13: 9783319676111
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Paperback. Condición: new. 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. Nº de ref. del artículo: 9783319676111
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