Authors:
- 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)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (12 chapters)
-
Front Matter
-
Background
-
Front Matter
-
-
Abstract Theory
-
Front Matter
-
-
Linear Theory
-
Front Matter
-
-
Nonlinear Problems
-
Front Matter
-
-
Back Matter
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
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
Book Title: Moving Interfaces and Quasilinear Parabolic Evolution Equations
Authors: Jan Prüss, Gieri Simonett
Series Title: Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-27698-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-27697-7Published: 03 August 2016
Softcover ISBN: 978-3-319-80196-4Published: 07 June 2018
eBook ISBN: 978-3-319-27698-4Published: 25 July 2016
Series ISSN: 1017-0480
Series E-ISSN: 2296-4886
Edition Number: 1
Number of Pages: XIX, 609
Number of Illustrations: 7 b/w illustrations
Topics: Partial Differential Equations, Mathematical Methods in Physics, Functional Analysis