LEADER 02593nam 2200589 450 001 996466476003316 005 20220909232613.0 010 $a3-540-46655-X 024 7 $a10.1007/BFb0090882 035 $a(CKB)1000000000437104 035 $a(SSID)ssj0000323880 035 $a(PQKBManifestationID)12124406 035 $a(PQKBTitleCode)TC0000323880 035 $a(PQKBWorkID)10303830 035 $a(PQKB)10155210 035 $a(DE-He213)978-3-540-46655-0 035 $a(MiAaPQ)EBC5595168 035 $a(Au-PeEL)EBL5595168 035 $a(OCoLC)1076237848 035 $a(MiAaPQ)EBC6842028 035 $a(Au-PeEL)EBL6842028 035 $a(OCoLC)793079282 035 $a(PPN)155164295 035 $a(EXLCZ)991000000000437104 100 $a20220909d1991 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe hyperbolic Cauchy problem /$fKunihiko Kajitani, Tatsuo Nishitani 205 $a1st ed. 1991. 210 1$aBerlin, Germany :$cSpringer,$d[1991] 210 4$dİ1991 215 $a1 online resource (VIII, 172 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1505 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-55018-6 330 $aThe approach to the Cauchy problem taken here by the authors is based on theuse of Fourier integral operators with a complex-valued phase function, which is a time function chosen suitably according to the geometry of the multiple characteristics. The correctness of the Cauchy problem in the Gevrey classes for operators with hyperbolic principal part is shown in the first part. In the second part, the correctness of the Cauchy problem for effectively hyperbolic operators is proved with a precise estimate of the loss of derivatives. This method can be applied to other (non) hyperbolic problems. The text is based on a course of lectures given for graduate students but will be of interest to researchers interested in hyperbolic partial differential equations. In the latter part the reader is expected to be familiar with some theory of pseudo-differential operators. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1505 606 $aCauchy problem 615 0$aCauchy problem. 676 $a510.8 700 $aKajitani$b Kunihiko$f1941-$059539 702 $aNishitani$b Tatsuo$f1950- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466476003316 996 $aHyperbolic cauchy problem$9262286 997 $aUNISA