Evolution Equations in Scales of Banach Spaces

  • Oliver┬áCaps

Part of the Teubner-Texte zur Mathematik book series (TTZM, volume 140)

Table of contents

  1. Front Matter
    Pages 1-12
  2. Oliver Caps
    Pages 13-25
  3. Oliver Caps
    Pages 27-77
  4. Oliver Caps
    Pages 130-165
  5. Back Matter
    Pages 295-309

About this book


The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem. Many applications illustrate the generality of the approach. In particular, using the Fefferman-Phong inequality unifying results on parabolic and hyperbolic equations generalizing classical ones and a unified treatment of Navier-Stokes and Euler equations is described. Assuming only basic knowledge in analysis and functional analysis the book provides all mathematical tools and is aimed for students, graduates, researchers, and lecturers.


Applications to quasilinear evolution equations Quasilinear evolution equations Tools from functional analysis Well-posedness functional analysis linear Cauchy problem

Authors and affiliations

  • Oliver┬áCaps
    • 1
  1. 1.MainzDeutschland

Bibliographic information

  • DOI
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2002
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-519-00376-2
  • Online ISBN 978-3-322-80039-8
  • Series Print ISSN 0138-502X
  • Buy this book on publisher's site