Progress in Nonlinear Differential Equations and Their Applications

Spectral Methods in Surface Superconductivity

Authors: Fournais, Søren, Helffer, Bernard

  • Covers groundbreaking results in the fast growing field of superconductivity
  • Provides a concrete introduction to PDEs and spectral methods
  • Covers both two- and three-dimensional cases of Ginzburg-Landau function extensively
  • Includes open problems
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eBook $54.99
price for USA (gross)
  • ISBN 978-0-8176-4797-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-8176-4796-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa.

Key topics and features of the work:

* Provides a concrete introduction to techniques in spectral theory and partial differential equations
* Offers a complete analysis of the two-dimensional Ginzburg–Landau functional with large kappa in the presence of a magnetic field
* Treats the three-dimensional case thoroughly
* Includes open problems

Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Reviews

From the reviews:

“The book is concerned with the analysis of mathematical problems connected with the theory of superconductivity. The authors consider a standard basic model of superconductivity described by the Ginzburg-Landau functional. … The authors attempt to make the book self-contained, having graduate students and researchers in mind. For this purpose, at the end of the book they add various appendices containing somewhat standard material. … The book concludes with a fairly complete bibliography on the subject.” (Yuri A. Kordyukov, Mathematical Reviews, Issue 2011 j)

Table of contents (16 chapters)

  • Spectral Analysis of Schrödinger Operators

    Fournais, Søren (et al.)

    Pages 3-17

  • Diamagnetism

    Fournais, Søren (et al.)

    Pages 19-30

  • Models in One Dimension

    Fournais, Søren (et al.)

    Pages 31-43

  • Constant Field Models in Dimension 2: Noncompact Case

    Fournais, Søren (et al.)

    Pages 45-50

  • Constant Field Models in Dimension 2: Discs and Their Complements

    Fournais, Søren (et al.)

    Pages 51-65

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-0-8176-4797-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-8176-4796-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Methods in Surface Superconductivity
Authors
Series Title
Progress in Nonlinear Differential Equations and Their Applications
Series Volume
77
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4797-1
DOI
10.1007/978-0-8176-4797-1
Hardcover ISBN
978-0-8176-4796-4
Series ISSN
1421-1750
Edition Number
1
Number of Pages
XX, 324
Number of Illustrations and Tables
2 b/w illustrations
Topics