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Moving Interfaces and Quasilinear Parabolic Evolution Equations

  • Jan Prüss
  • Gieri Simonett

Part of the Monographs in Mathematics book series (MMA, volume 105)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Background

    1. Front Matter
      Pages 1-1
    2. Jan Prüss, Gieri Simonett
      Pages 3-41
    3. Jan Prüss, Gieri Simonett
      Pages 43-86
  3. Abstract Theory

    1. Front Matter
      Pages 87-87
    2. Jan Prüss, Gieri Simonett
      Pages 89-147
    3. Jan Prüss, Gieri Simonett
      Pages 149-194
    4. Jan Prüss, Gieri Simonett
      Pages 195-230
  4. Linear Theory

    1. Front Matter
      Pages 231-231
    2. Jan Prüss, Gieri Simonett
      Pages 233-310
    3. Jan Prüss, Gieri Simonett
      Pages 311-361
    4. Jan Prüss, Gieri Simonett
      Pages 363-416
  5. Nonlinear Problems

    1. Front Matter
      Pages 417-417
    2. Jan Prüss, Gieri Simonett
      Pages 419-450
    3. Jan Prüss, Gieri Simonett
      Pages 451-490
    4. Jan Prüss, Gieri Simonett
      Pages 491-513
    5. Jan Prüss, Gieri Simonett
      Pages 515-570
  6. Back Matter
    Pages 571-609

About this book

Introduction

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis.

The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Keywords

partial differential equations maximal regularity evolution equations moving interfaces two-phase fluid flows Navier-Stokes equations phase transitions entropy and thermodynamics geometry of moving hypersurfaces transmissions problems vector-­valued harmonic analysis

Authors and affiliations

  • Jan Prüss
    • 1
  • Gieri Simonett
    • 2
  1. 1.Institut für MathematikMartin-Luther-Universität Halle-WittenbeHalle (Saale)Germany
  2. 2.Dept of MathematicsVanderbilt UnivNashvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27698-4
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-27697-7
  • Online ISBN 978-3-319-27698-4
  • Series Print ISSN 1017-0480
  • Series Online ISSN 2296-4886
  • Buy this book on publisher's site