Overview
- Affordable, softcover reprint of a classic textbook
- Authors are well-known specialists in nonlinear functional analysis and partial differential equations
- Written in a clear, readable style with many examples
Part of the book series: Modern Birkhäuser Classics (MBC)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (11 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero.
One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized.
The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis,partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.
Authors and Affiliations
Bibliographic Information
Book Title: Ginzburg-Landau Vortices
Authors: Fabrice Bethuel, Haim Brezis, Frederic Helein
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-3-319-66673-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-66672-3Published: 05 October 2017
eBook ISBN: 978-3-319-66673-0Published: 21 September 2017
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XXIX, 159
Number of Illustrations: 4 b/w illustrations, 1 illustrations in colour
Topics: Partial Differential Equations, Mathematical Applications in the Physical Sciences