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- catalog abstract "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.".
- catalog contributor b3469651.
- catalog contributor b3469652.
- catalog created "c1991.".
- catalog date "1991".
- catalog date "c1991.".
- catalog dateCopyrighted "c1991.".
- catalog description "Includes bibliographical references and index.".
- catalog description "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.".
- catalog extent "vi, 167 p. ;".
- catalog identifier "0387550186 (U.S.)".
- catalog identifier "3540550186".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1505.".
- catalog isPartOf "Lecture notes in mathematics ; 1505".
- catalog issued "1991".
- catalog issued "c1991.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog subject "Cauchy problem.".
- catalog subject "Differential equations, Hyperbolic.".
- catalog subject "Fourier integral operators.".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Mathematics.".
- catalog subject "Partial differential operators.".
- catalog title "The hyperbolic Cauchy problem / Kunihiko Kajitani, Tatsuo Nishitani.".
- catalog type "text".