The approach to the Cauchy problem taken here by the authors is based on theuse of Fourier integral operators with a complex-valued phase function, which is a time function chosen suitably according to the geometry of the multiple characteristics. The correctness of the Cauchy problem in the Gevrey classes for operators with hyperbolic principal part is shown in the first part. In the second part, the correctness of the Cauchy problem for effectively hyperbolic operators is proved with a precise estimate of the loss of derivatives. This method can be applied to other (non) hyperbolic problems. The text is based on a course of lectures given for graduate students but will be of interest to researchers interested in hyperbolic partial differential equations. In the latter part the reader is expected to be familiar with some theory of pseudo-differential operators.
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Fourier integral operators with complex-valued phase function and the Cauchy problem for hyperbolic operators.- The effectively hyperbolic Cauchy problem.
Book by Kajitani Kunihiko Nishitani Tatsuo
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The approach to the Cauchy problem taken here by the authorsis based on theuse of Fourier integral operators with acomplex-valued phase function, which is a time functionchosen suitably according to the geometry of the multiplecharacteristics. The correctness of the Cauchy problem inthe Gevrey classes for operators with hyperbolic principalpart is shown in the first part. In the second part, thecorrectness of the Cauchy problem for effectively hyperbolicoperators is proved with a precise estimate of the loss ofderivatives. This method can be applied to other (non)hyperbolic problems. The text is based on a course oflectures given for graduate students but will be of interestto researchers interested in hyperbolic partial differentialequations. In the latter part the reader is expected to befamiliar with some theory of pseudo-differential operators. 180 pp. Englisch. Codice articolo 9783540550181
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167 Seiten, 3540550186 Sprache: Englisch Gewicht in Gramm: 240 Groß 8°, Original-Karton (Softcover), Bibliotheks-Exemplar (ordnungsgemäß entwidmet), Stempel auf Titel, insgesamt gutes und innen sauberes Exemplar, Codice articolo 81780
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