Ginzburg-Landau Vortices (Paperback, 1994 ed.)

The original motivation of this study comes from the following questions that were mentioned to one ofus by H. Matano. Let 2 2 G= B = {x=(X1lX2) E 2; x~ + x~ = Ixl < 1}. 1 Consider the Ginzburg-Landau functional 2 2 (1) E~(u) = ~ LIVul + 4~2 L(lu1 _1)2 which is defined for maps u E H1(G;C) also identified with Hl(G;R2). Fix the boundary condition 9(X) =X on 8G and set H; = {u E H1(G;C); u = 9 on 8G}. It is easy to see that (2) is achieved by some u~ that is smooth and satisfies the Euler equation in G, -~u~ = :2 u~(1 _lu~12) (3) { on aGo u~ =9 Themaximum principleeasily implies (see e.g., F. Bethuel, H. Brezisand F. Helein (2]) that any solution u~ of (3) satisfies lu~1 ~ 1 in G. In particular, a subsequence (u~,.) converges in the w* - LOO(G) topology to a limit u*.

General

Imprint:	Birkhauser Boston
Country of origin:	United States
Series:	Progress in Nonlinear Differential Equations and Their Applications, 13
Release date:	March 1994
First published:	1994
Authors:	Fabrice Bethuel • Haim Brezis • Frederic Helein
Dimensions:	235 x 155 x 11mm (L x W x T)
Format:	Paperback
Pages:	162
Edition:	1994 ed.
ISBN-13:	978-0-8176-3723-1
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	0-8176-3723-0
Barcode:	9780817637231

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