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Studies in Non-Linear Stability Theory

  • Wiktor Eckhaus

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 6)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Wiktor Eckhaus
    Pages 1-10
  3. Wiktor Eckhaus
    Pages 19-28
  4. Wiktor Eckhaus
    Pages 43-52
  5. Wiktor Eckhaus
    Pages 63-76
  6. Wiktor Eckhaus
    Pages 77-96
  7. Wiktor Eckhaus
    Pages 97-113
  8. Back Matter
    Pages 114-117

About this book

Introduction

Non-linear stability problems formulated in terms of non-linear partial differential equations have only recently begun to attract attention and it will probably take some time before our understanding of those problems reaches some degree of maturity. The passage from the more classical linear analysis to a non-linear analysis increases the mathematical complexity of the stability theory to a point where it may become discouraging, while some of the more usual mathematical methods lose their applicability. Although considerable progress has been made in recent years, notably in the field of fluid mechanics, much still remains to be done before a more permanent outline of the subject can be established. I have not tried to present in this monograph an account of what has been accomplished, since the rapidly changing features of the field make the periodical literature a more appropriate place for such a review. The aim of this book is to present one particular line of research, originally developed in a series of papers published in 'Journal de Mecanique' 1962-1963, in which I attempted to construct a mathematical theory for certain classes of non-linear stability problems, and to gain some understanding of the non-linear phenomena which are involved. The opportunity to collect the material in this volume has permitted a more coherent presentation, while various points of the analysis have been developed in greater detaiL I hope that a more unified form of the theory has thus been achieved.

Keywords

Systemtheorie differential equation instability mechanics operations research partial differential equation stability stability theory systems theory turbulence

Authors and affiliations

  • Wiktor Eckhaus
    • 1
  1. 1.Département de MécaniqueUniversité de ParisParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-88317-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1965
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-88319-4
  • Online ISBN 978-3-642-88317-0
  • Series Print ISSN 0081-3877
  • Buy this book on publisher's site