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Spectral methods in surface superconductivity. (English) Zbl 1256.35001

Progress in Nonlinear Differential Equations and Their Applications 77. Basel: Birkhäuser (ISBN 978-0-8176-4796-4/hbk; 978-0-8176-4797-1/ebook). xx, 324 p. (2010).
Publisher’s description: 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 are:
– 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.

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35P15 Estimates of eigenvalues in context of PDEs
35Q56 Ginzburg-Landau equations
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