Cauchy Problem Differential Operators by Nishitani Tatsuo (19 results)

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Paperback. Condition: 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.

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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 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 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.

Paperback. Condition: 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 our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 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 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. 224 pp. Englisch.

Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 numero.

Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 224 pp. Englisch.