03369nam 22005895 450 991030015390332120200701061104.03-319-02273-310.1007/978-3-319-02273-4(CKB)3710000000078595(DE-He213)978-3-319-02273-4(SSID)ssj0001067537(PQKBManifestationID)11598589(PQKBTitleCode)TC0001067537(PQKBWorkID)11091518(PQKB)10947686(MiAaPQ)EBC3107095(PPN)176105743(EXLCZ)99371000000007859520131118d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierHyperbolic Systems with Analytic Coefficients Well-posedness of the Cauchy Problem /by Tatsuo Nishitani1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (VIII, 237 p.) Lecture Notes in Mathematics,0075-8434 ;2097Bibliographic Level Mode of Issuance: Monograph3-319-02272-5 Introduction -- Necessary conditions for strong hyperbolicity -- Two by two systems with two independent variables -- Systems with nondegenerate characteristics -- Index.This 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.  .Lecture Notes in Mathematics,0075-8434 ;2097Differential equations, PartialPhysicsPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Differential equations, Partial.Physics.Partial Differential Equations.Mathematical Methods in Physics.515.353Nishitani Tatsuoauthttp://id.loc.gov/vocabulary/relators/aut59540MiAaPQMiAaPQMiAaPQBOOK9910300153903321Hyperbolic systems with analytic coefficients820703UNINA