Mainini, Edoardo:
A Global Uniqueness Result for an Evolution Problem Arising in Superconductivity
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.2, p. 509-528, (English)
pdf (167 Kb), djvu (167 Kb). | MR 2537285 | Zbl 1175.82080
Sunto
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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