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Evolutionary Integral Equations and Applications

  • Jan Prüss

Part of the Monographs in Mathematics book series (MMA, volume 87)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Equations of Scalar Type

    1. Front Matter
      Pages 29-29
    2. Jan Prüss
      Pages 30-48
    3. Jan Prüss
      Pages 49-67
    4. Jan Prüss
      Pages 68-89
    5. Jan Prüss
      Pages 90-121
    6. Jan Prüss
      Pages 122-150
  3. Nonscalar Equations

    1. Front Matter
      Pages 151-151
    2. Jan Prüss
      Pages 152-184
    3. Jan Prüss
      Pages 185-211
    4. Jan Prüss
      Pages 212-235
  4. Equations on the Line

    1. Front Matter
      Pages 255-255
    2. Jan Prüss
      Pages 256-283
    3. Jan Prüss
      Pages 284-305
    4. Jan Prüss
      Pages 306-322
    5. Jan Prüss
      Pages 323-345
  5. Back Matter
    Pages 347-369

About this book

Introduction

During the last two decades the theory of abstract Volterra equations has under­ gone rapid development. To a large extent this was due to the applications of this theory to problems in mathematical physics, such as viscoelasticity, heat conduc­ tion in materials with memory, electrodynamics with memory, and to the need of tools to tackle the problems arising in these fields. Many interesting phenomena not found with differential equations but observed in specific examples of Volterra type stimulated research and improved our understanding and knowledge. Al­ though this process is still going on, in particular concerning nonlinear problems, the linear theory has reached a state of maturity. In recent years several good books on Volterra equations have appeared. How­ ever, none of them accounts for linear problems in infinite dimensions, and there­ fore this part of the theory has been available only through the - meanwhile enor­ mous - original literature, so far. The present monograph intends to close this gap. Its aim is a coherent exposition of the state of the art in the linear theory. It brings together and unifies most of the relevant results available at present, and should ease the way through the original literature for anyone intending to work on abstract Volterra equations and its applications. And it exhibits many prob­ lems in the linear theory which have not been solved or even not been considered, so far.

Keywords

differential equation ergodic theory function space hyperbolic equation Integral Integral equation

Authors and affiliations

  • Jan Prüss
    • 1
  1. 1.Universität-GH PaderbornPaderbornGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-8570-6
  • Copyright Information Birkhäuser Verlag Basel 1993
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-7643-2876-4
  • Online ISBN 978-3-0348-8570-6
  • Series Print ISSN 1017-0480
  • Series Online ISSN 2296-4886
  • Buy this book on publisher's site