Geodesic
A Global Uniqueness Result for an Evolution Problem Arising in Superconductivity
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 509-528

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We consider an energy functional on measures in $\mathbb{R}^{2}$ arising in superconductivity as a limit case of the well-known Ginzburg Landau functionals. We study its gradient flow with respect to the Wasserstein metric of probability measures, whose corresponding time evolutive problem can be seen as a mean field model for the evolution of vortex densities. Improving the analysis made in [AS], we obtain a new existence and uniqueness result for the evolution problem. 
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     author = {Mainini, Edoardo},
     title = {A {Global} {Uniqueness} {Result} for an {Evolution} {Problem} {Arising} in {Superconductivity}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {509--528},
     publisher = {mathdoc},
     volume = {Ser. 9, 2},
     number = {2},
     year = {2009},
     zbl = {1175.82080},
     mrnumber = {2537285},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a13/}
}
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Mainini, Edoardo. A Global Uniqueness Result for an Evolution Problem Arising in Superconductivity. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 509-528. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a13/