Lectures on Nonlinear Evolution Equations

Initial Value Problem

  • Reinhard Racke

Part of the Aspects of Mathematics book series (ASMA, volume 19)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Reinhard Racke
    Pages 1-6
  3. Reinhard Racke
    Pages 21-33
  4. Reinhard Racke
    Pages 34-57
  5. Reinhard Racke
    Pages 79-83
  6. Reinhard Racke
    Pages 84-90
  7. Reinhard Racke
    Pages 91-105
  8. Reinhard Racke
    Pages 106-109
  9. Reinhard Racke
    Pages 110-113
  10. Reinhard Racke
    Pages 114-211
  11. Reinhard Racke
    Pages 212-225
  12. Back Matter
    Pages 226-260

About this book

Introduction

The book in hand is based on lectures which were given at the University of Bonn in the winter semesters of 1989/90 and 1990/91. The aim of the lectures was to present an elementary, self-contained introduction into some important aspects of the theory of global, small, smooth solutions to initial value problems for non linear evolution equa­ tions. The addressed audience included graduate students of both mathematics and physics who were only assumed to have abasie knowledge of linear partial differential equations. Thus, in the spirit of the underlying series, this book is intended to serve as a detailed basis for lectures on the subject as weIl as for self-studies for students or for other newcomers to this field. The presentation of the theory is made using the classical method of continuation of local solutions with the help of apriori estimates obtained for small data. The corre­ sponding global existence theorems have been proved mainly in the last decade, focussing on fully nonlinear systems; Related questions concerning large data problems, the ex­ istence of weak solutions or the analysis of &.hock waves are not discussed. Also the question of optimal regularity assumptions on the coefficients is beyond the scope of the book and is touched only in part and exemplarily.

Keywords

a priori estimates equation evolution global solutions hyperbolic system initial value problems interpolation local solutions nonlinear evolution equations online presentation proof theorem

Authors and affiliations

  • Reinhard Racke
    • 1
  1. 1.Institute of Applied MathematicsUniversity of BonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-663-10629-6
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 1992
  • Publisher Name Vieweg+Teubner Verlag, Wiesbaden
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-663-10631-9
  • Online ISBN 978-3-663-10629-6
  • Series Print ISSN 0179-2156
  • About this book
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