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A gradient flow approach to an evolution problem arising in superconductivity

✍ Scribed by Ambrosio, Luigi (author);Serfaty, Sylvia (author)

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
331 KB
Volume
61
Category
Article
ISSN
0010-3640

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✦ Synopsis

Abstract

We study an evolution equation proposed by Chapman, Rubinstein, and Schatzman as a mean‐field model for the evolution of the vortex density in a superconductor. We treat the case of a bounded domain where vortices can exit or enter the domain. We show that the equation can be derived rigorously as the gradient flow of some specific energy for the Riemannian structure induced by the Wasserstein distance on probability measures. This leads us to some existence and uniqueness results and energy‐dissipation identities. We also exhibit some β€œentropies” that decrease through the flow and allow us to get regularity results (solutions starting in L^p^, p > 1, remain in L^p^). Β© 2007 Wiley Periodicals, Inc.

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