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Hyperbolic systems with analytic coefficients : well-posedness of the Cauchy problem

Author: Tatsuo Nishitani
Publisher: Cham : Springer, 2014.
Series: Lecture notes in mathematics (Springer-Verlag), 2097.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tatsuo Nishitani
ISBN: 9783319022734 3319022733
OCLC Number: 868827115
Description: 1 online resource (viii, 237 pages).
Contents: Necessary conditions for strong hyperbolicity --
Two by two systems with two independent variables --
Systems with nondegenerate characteristics.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2097.
Responsibility: Tatsuo Nishitani.
More information:

Abstract:

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.

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