Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2097)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (4 chapters)
Keywords
About this book
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 contain 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.
Â
Authors and Affiliations
Bibliographic Information
Book Title: Hyperbolic Systems with Analytic Coefficients
Book Subtitle: Well-posedness of the Cauchy Problem
Authors: Tatsuo Nishitani
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-02273-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Softcover ISBN: 978-3-319-02272-7Published: 05 December 2013
eBook ISBN: 978-3-319-02273-4Published: 19 November 2013
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 237
Topics: Partial Differential Equations, Mathematical Methods in Physics