03285nam a2200433 i 4500991003576719707536m o d cr nn||||mamaa181127s2017 gw a o 000 0 eng d978331967612833196761219783319676111331967611310.1007/978-3-319-67612-8doib14354470-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.35323AMS 35-02LC QA370-380Nishitani, Tatsuo59540Cauchy Problem for Differential Operators with Double Characteristics[e-book]:Non-Effectively Hyperbolic Characteristics /Tatsuo NishitaniCham :Springer,20171 online resource (viii, 211 pages) :illustrationstexttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture Notes in Mathematics,0075-8434 ;2202Includes bibliographical references and index1. Introduction ; 2 Non-effectively hyperbolic characteristics.- 3 Geometry of bicharacteristics.- 4 Microlocal energy estimates and well-posedness.- 5 Cauchy problemno tangent bicharacteristics. - 6 Tangent bicharacteristics and ill-posedness.- 7 Cauchy problem in the Gevrey classes.- 8 Ill-posed Cauchy problem, revisited ; ReferencesCombining 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 eigenvalues. 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 Pæj and P æj , where iæj are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 ₉ 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 roleDifferential equations, PartialOrdinary Differential EquationsPrinted edition:9783319676111https://link.springer.com/book/10.1007/978-3-319-67612-8#tocAn electronic book accessible through the World Wide Web.b1435447007-04-2227-11-18991003576719707536Cauchy problem for differential operators with double characteristics1522944UNISALENTOle01327-11-18m@ -enggw 00