Overview
- 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)
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Front Matter
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Background
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Front Matter
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Abstract Theory
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Front Matter
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Linear Theory
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Front Matter
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Nonlinear Problems
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Front Matter
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Back Matter
Keywords
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.
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Authors and Affiliations
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