This book is concerned with the study in two dimensions of stationary solutions of u? of a complex valued Ginzburg-Landau equation involving a small parameter ?. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ? has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ? tends to zero.
One of the main results asserts that the limit u-star of minimizers u? 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.
| ISBN: | 9783319666723 |
| Publication date: | 5th October 2017 |
| Author: | Fabrice Bethuel, Haïm Brezis, Frédéric Hélein |
| Publisher: | Birkhauser an imprint of Springer International Publishing |
| Format: | Paperback |
| Pagination: | 159 pages |
| Series: | Modern Birkhäuser Classics |
| Genres: |
Differential calculus and equations Mathematical physics |