Ginzburg-Landau Vortices (Paperback, 1st ed. 2017)

This book is concerned with the study in two dimensions of stationary solutions of ue of a complex valued Ginzburg-Landau equation involving a small parameter e. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter e has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as e tends to zero. One of the main results asserts that the limit u-star of minimizers ue 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.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Modern Birkhauser Classics
Release date:	October 2017
First published:	2017
Authors:	Fabrice Bethuel • Haim Brezis • Frederic Helein
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	159
Edition:	1st ed. 2017
ISBN-13:	978-3-319-66672-3
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling Promotions
LSN:	3-319-66672-X
Barcode:	9783319666723

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