02984nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001700186072002300203082001600226100003200242245013700274264007500411300003500486336002600521337002600547338003600573347002400609490005300633505017500686520110500861650001701966650003701983650002602020650001702046650003602063650003702099710003402136773002002170776003602190830005302226856004802279912001402327912001402341950004802355999001502403952008402418978-3-319-02273-4DE-He21320150803155057.0cr nn 008mamaa131118s2014 gw | s |||| 0|eng d a97833190227349978-3-319-02273-47 a10.1007/978-3-319-02273-42doi 4aQA370-380 7aPBKJ2bicssc 7aMAT0070002bisacsh04a515.3532231 aNishitani, Tatsuo.eauthor.10aHyperbolic Systems with Analytic Coefficientsh[electronic resource] :bWell-posedness of the Cauchy Problem /cby Tatsuo Nishitani. 1aCham :bSpringer International Publishing :bImprint: Springer,c2014. aVIII, 237 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aLecture Notes in Mathematics,x0075-8434 ;v20970 aIntroduction -- Necessary conditions for strong hyperbolicity -- Two by two systems with two independent variables -- Systems with nondegenerate characteristics -- Index. aThis 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 nearby. 0aMathematics. 0aDifferential equations, partial. 0aMathematical physics.14aMathematics.24aPartial Differential Equations.24aMathematical Methods in Physics.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783319022727 0aLecture Notes in Mathematics,x0075-8434 ;v209740uhttp://dx.doi.org/10.1007/978-3-319-02273-4 aZDB-2-SMA aZDB-2-LNM aMathematics and Statistics (Springer-11649) c6948d6948 00104070918511aMAINbMAINd2015-08-03o515.353r2015-08-03w2015-08-03yEBK