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Qualitative study of radial solutions of the Ginzburg-Landau system in RN (N ≥ 3)

✍ Scribed by A Farina; M Guedda

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
254 KB
Volume
13
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this work, we are interested in solutions w : R N --~ ~(N, N > 3, to Ginzburg-Landau system --Aw = w(1 --]w12), having the form w(x) = u(ixi)g(x/Ixl). By using a shooting argument, we prove the existence of three families of profiles u and investigate its properties. In particular, we shall show that, for any admissible function g, there exists a unique positive solution 'u 9 which approaches 1 as Ix I ---* +oz.

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Uniqueness of weak solutions in critical
Uniqueness of weak solutions in critical space of the 3-D time-dependent Ginzburg-Landau equations for superconductivity
✍ Jishan Fan; Hongjun Gao 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB 👁 1 views

## Abstract We prove the uniqueness of weak solutions of the 3‐D time‐dependent Ginzburg‐Landau equations for super‐conductivity with initial data (__ψ__~0~, __A__~0~)∈ __L__^2^ under the hypothesis that (__ψ__, __A__) ∈ __L__^__s__^(0, __T__; __L__^__r__,∞^) ×$ L^{\bar s} $(0, __T__;$ L^{\bar r,