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Ginzburg-Landau Vortices Edition: 1
Ginzburg-Landau Vortices Edition: 1
Fabrice Bethuel, Haim Brezis, Frederic Helein (auth.)
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This book is concerned with the study in two dimensions of stationary solutions of u ɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero. One of the main results asserts that the limit u-star of minimizers u ɛ 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.
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Year:
2022
Publisher:
Birkhäuser City: Cham
Language:
English
ISBN 10:
1461202876
ISBN 13:
9781461202875
ISBN:
9783319666730, 3319666738, 9783319666723, 331966672X, 9780817637231, 0817637230, 9781461202875, 1461
Series:
Modern Birkhäuser Classics
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