02819nmm a2200421 i 4500991003324949707536cr cn ---mpcbr170207s2014 sz | o j |||| 0|eng d9783319022734 (ebook)10.1007/978-3-319-02273-4doib14316171-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.35323AMS 35L45AMS 35L40AMS 35L55Nishitani, Tatsuo59540Hyperbolic Systems with Analytic Coefficients[e-book] :Well-posedness of the Cauchy Problem /by Tatsuo NishitaniCham :Springer Intern. Publ.,20141 online resource (viii, 237 p.)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture Notes in Mathematics,1617-9692 ;2097Introduction ; Necessary conditions for strong hyperbolicity ; Two by two systems with two independent variables ; Systems with nondegenerate characteristics ; IndexThis monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearbyDifferential equations, partialMathematical physicsSpringerLink (Online service)Springer eBooks.Printed edition:9783319022727.http://link.springer.com/book/10.1007/978-3-319-02273-4An electronic book accessible through the World Wide.b1431617103-03-2207-02-17991003324949707536Hyperbolic systems with analytic coefficients820703UNISALENTOle01307-02-17m@ -engsz 00