Hyperbolic Systems with Analytic Coefficients

Well-posedness of the Cauchy Problem

  • Tatsuo┬áNishitani
Part of the Lecture Notes in Mathematics book series (LNM, volume 2097)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Tatsuo Nishitani
    Pages 1-29
  3. Tatsuo Nishitani
    Pages 31-84
  4. Tatsuo Nishitani
    Pages 161-229
  5. Back Matter
    Pages 231-240

About this book

Introduction

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.

 

Keywords

35L45,35L40,35L55 Cauchy problem Hyperbolic systems Real analytic coefficients Strongly hyperbolic Well-posedness

Authors and affiliations

  • Tatsuo┬áNishitani
    • 1
  1. 1.Department of MathematicsGraduate School of Science, Osaka UniversityToyonaka, OsakaJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-02273-4
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02272-7
  • Online ISBN 978-3-319-02273-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book