Overview
- Describes essential mathematical techniques and tools for analyzing the Ginzburg--Landau functional
- Presents an introduction to the theory with results and current research
- Acts a guide to the various branches of Ginzburg-Landau studies and provides context for the study of vortices
- Includes list of open problems
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 70)
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Table of contents (15 chapters)
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"This book deals with the mathematical study of the two-dimensional Ginzburg-Landau model with magnetic field. This important model was introduced by Ginzburg and Landau in the 1950s as a phenomenological model to describe superconductivity consisting in the complete loss of resistivity of certain metals and alloys at very low temperatures...All parts of this interesting book are clearly and rigorously written. A consistent bibliography is given and several open problems are detailed. This work has to be recommended."
—Zentralblatt MATH
"In conclusion, this book is an excellent, up-to-the-minute presentation of the current state of the mathematics of vortices in Ginzburg-Landau models. It also represents a tour de force of mathematical analysis, revealing a fascinating and intricate picture of a physical model which may have been unexpected based on heuristic considerations. I strongly recommend this book to researchers who are interested in vortices (andother quantized singularities) as these methods will continue to be instrumental in forthcoming research in the field. One could also find interesting material to supplement a graduate coursc in variational methods or PDEs."
—SIAM Review
Authors and Affiliations
Bibliographic Information
Book Title: Vortices in the Magnetic Ginzburg-Landau Model
Authors: Etienne Sandier, Sylvia Serfaty
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-0-8176-4550-2
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkh�user Boston 2007
Hardcover ISBN: 978-0-8176-4316-4Published: 19 December 2006
eBook ISBN: 978-0-8176-4550-2Published: 14 May 2008
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XII, 322
Number of Illustrations: 13 b/w illustrations
Topics: Partial Differential Equations, Theoretical, Mathematical and Computational Physics, Functions of a Complex Variable