Hyperbolic systems with analytic coefficients [electronic resource] : well-posedness of the Cauchy problem / Tatsuo Nishitani.
Nishitani, Tatsuo, 1950-, author.
2014
QA377
Available Online

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Title Hyperbolic systems with analytic coefficients [electronic resource] : well-posedness of the Cauchy problem / Tatsuo Nishitani.
Author Nishitani, Tatsuo, 1950-, author.
ISBN 9783319022734 electronic book
3319022733 electronic book
9783319022727
3319022725
DOI https://doi.org/10.1007/978-3-319-02273-4
Published Cham : Springer, 2014.
Language English
Description 1 online resource (viii, 237 pages).
Item Number 10.1007/978-3-319-02273-4 doi
Call Number QA377
Dewey Decimal Classification 515/.35
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on online resource; title from PDF title page (SpringerLink, viewed November 25, 2013).
Series Lecture notes in mathematics (Springer-Verlag) ; 2097.
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Necessary conditions for strong hyperbolicity
Two by two systems with two independent variables
Systems with nondegenerate characteristics.

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