Ginzburg-Landau Vortices: 13 (Progress in Nonlinear Differential Equations and Their Applications, 13) - Image 1

£72.66

Birkhauser Ginzburg-Landau Vortices: 13 (Progress in Nonlinear Differential Equations and Their Applications, 13)

Name: Ginzburg-Landau Vortices: 13 (Progress in Nonlinear Differential Equations and Their Applications, 13)
Brand: Birkhauser
Price: 72.66 GBP
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Engineering Physics

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Description

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*.

Product Specifications

Brand: Birkhauser
Format: paperback
ASIN: 0817637230
Category: Books > Subjects > Science, Nature & Maths > Engineering & Technology > Engineering Physics
Domain: Amazon UK
Publication Date: 28 March 1994
Listed Since: 12 January 2007

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Birkhauser Ginzburg-Landau Vortices: 13 (Progress in Nonlinear Differential Equations and Their Applications, 13)

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