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  • Book
  • © 2016

Moving Interfaces and Quasilinear Parabolic Evolution Equations

Birkhäuser
  • Provides a rich source of techniques and results
  • Presents an in-depth and up-to-date exposition of the theory of maximal regularity and its application to quasilinear parabolic equations
  • Demonstrates how the theory is applied to problems involving moving interphases and a variety of geometric evolution equations
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xix
  2. Background

    1. Front Matter

      Pages 1-1
    2. Problems and Strategies

      • Jan Prüss, Gieri Simonett
      Pages 3-41
    3. Tools from Differential Geometry

      • Jan Prüss, Gieri Simonett
      Pages 43-86
  3. Abstract Theory

    1. Front Matter

      Pages 87-87
    2. Operator Theory and Semigroups

      • Jan Prüss, Gieri Simonett
      Pages 89-147
    3. Vector-Valued Harmonic Analysis

      • Jan Prüss, Gieri Simonett
      Pages 149-194
    4. Quasilinear Parabolic Evolution Equations

      • Jan Prüss, Gieri Simonett
      Pages 195-230
  4. Linear Theory

    1. Front Matter

      Pages 231-231
    2. Elliptic and Parabolic Problems

      • Jan Prüss, Gieri Simonett
      Pages 233-310
    3. Generalized Stokes Problems

      • Jan Prüss, Gieri Simonett
      Pages 311-361
    4. Two-Phase Stokes Problems

      • Jan Prüss, Gieri Simonett
      Pages 363-416
  5. Nonlinear Problems

    1. Front Matter

      Pages 417-417
    2. Local Well-Posedness and Regularity

      • Jan Prüss, Gieri Simonett
      Pages 419-450
    3. Linear Stability of Equilibria

      • Jan Prüss, Gieri Simonett
      Pages 451-490
    4. Qualitative Behaviour of the Semiflows

      • Jan Prüss, Gieri Simonett
      Pages 491-513
    5. Further Parabolic Evolution Problems

      • Jan Prüss, Gieri Simonett
      Pages 515-570
  6. Back Matter

    Pages 571-609

About this book

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 offluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Reviews

“This book is useful for readers at a variety of levels and stages. … The book includes an extensive bibliography and bibliographical remarks throughout that serve to situate the book perfectly within its context. … the work serves as an invaluable resource to the community.” (Glen E. Wheeler, Mathematical Reviews, October, 2017)

Authors and Affiliations

  • Institut für Mathematik, Martin-Luther-Universität Halle-Wittenbe, Halle (Saale), Germany

    Jan Prüss

  • Dept of Mathematics, Vanderbilt Univ, Nashville, USA

    Gieri Simonett

Bibliographic Information

Buy it now

Buying options

eBook USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access