Spectral Methods in Surface Superconductivity [Hardcover]

This book examines in detail the nonlinear GinzburgLandau 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 GinzburgLandau parameter kappa. 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.

In this book, two expert researchers present a comprehensive treatment of key results concerning the Ginzburg-Landau (GL) functional. Coverage examines in detail the two- and three-dimensional cases of the GL functional as they pertain to superconductivity.

In the past decade, the mathematics of superconductivity has been the subject of intense study. This book examines in detail the nonlinear GinzburgLandau (GL) functional, the model most commonly used. Specifically, cases in the presence of a strong magnetic field and with a sufficiently large GL parameter kappa are covered.

Key topics and features:

*Provides a concrete introduction to techniques in spectral theory and PDEs

*Offers a complete analysis of the two-dimensional GL-functional with large kappa in the presence of a magnetic field

*Treats the three-dimensional case thoroughly

*Includes exercises and open problems

Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate level understanding of functional analysis, spectral theory,lÓà