02593nam 2200589 450 99646647600331620220909232613.03-540-46655-X10.1007/BFb0090882(CKB)1000000000437104(SSID)ssj0000323880(PQKBManifestationID)12124406(PQKBTitleCode)TC0000323880(PQKBWorkID)10303830(PQKB)10155210(DE-He213)978-3-540-46655-0(MiAaPQ)EBC5595168(Au-PeEL)EBL5595168(OCoLC)1076237848(MiAaPQ)EBC6842028(Au-PeEL)EBL6842028(OCoLC)793079282(PPN)155164295(EXLCZ)99100000000043710420220909d1991 uy 0engurnn|008mamaatxtccrThe hyperbolic Cauchy problem /Kunihiko Kajitani, Tatsuo Nishitani1st ed. 1991.Berlin, Germany :Springer,[1991]©19911 online resource (VIII, 172 p.) Lecture Notes in Mathematics,0075-8434 ;1505Bibliographic Level Mode of Issuance: Monograph3-540-55018-6 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.Lecture Notes in Mathematics,0075-8434 ;1505Cauchy problemCauchy problem.510.8Kajitani Kunihiko1941-59539Nishitani Tatsuo1950-MiAaPQMiAaPQMiAaPQBOOK996466476003316Hyperbolic cauchy problem262286UNISA