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＜電子ブック＞
Hyperbolic Systems with Analytic Coefficients : Well-posedness of the Cauchy Problem / by Tatsuo Nishitani
(Lecture Notes in Mathematics. ISSN:16179692 ; 2097)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
大きさ	VIII, 237 p : online resource
著者標目	*Nishitani, Tatsuo author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical physics FREE:Differential Equations FREE:Mathematical Methods in Physics
一般注記	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.   HTTP:URL=https://doi.org/10.1007/978-3-319-02273-4

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