We prove that the global minimizer of the Ginzburg-Landau functional of superconductors in an external magnetic field is, below the first critical field, the vortex-less solution found in (S. Serfaty, to appear). © 2000 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. -On montre que le minim
Remarks on the existence of global minimizers for the Ginzburg–Landau energy functional
✍ Scribed by T. Giorgi; R.G. Smits
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 111 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0362-546X
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We study the following generalized 1D Ginzburg-Landau equation on Ω = (0, ∞) × (0, ∞): with initial and Dirichlet boundary conditions u(x, 0) = h(x), u(0, t) = Q(t). Based on detail analysis, the sharper existence and uniqueness of global solutions are obtained under sufficient conditions.
The Sobolev gradient technique has been discussed previously in this journal as an efficient method for finding energy minima of certain Ginzburg-Landau type functionals [S. Sial, J. Neuberger, T. Lookman, A. Saxena, Energy minimization using Sobolev gradients: application to phase separation and or
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