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Item Details
| Title:
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GINZBURG-LANDAU VORTICES
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| By: |
Fabrice Bethuel, Haim Brezis, Frederic Helein |
| Format: |
Paperback |
| List price:
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£99.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0817637230 |
| ISBN 13: |
9780817637231 |
| Publisher: |
BIRKHAUSER BOSTON INC |
| Pub. date: |
28 March, 1994 |
| Edition: |
1994 ed. |
| Series: |
Progress in Nonlinear Differential Equations and Their Applications 13 |
| Pages: |
162 |
| Description: |
The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on modern materials research. |
| Synopsis: |
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*. |
| Illustrations: |
XXVII, 162 p. |
| Publication: |
US |
| Imprint: |
Birkhauser Boston Inc |
| Returns: |
Returnable |
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