Michelle Schatzman, Courant, New York University
"Superconductivity in multiply connected thin domains"
he limit of Ginzburg-Landau equations of superconductivity on a thin domain as the thickness tends to zero is a problem defined on a geometrical graph; the transmission conditions at the vertices of the graph are Kirchhof-type conditions; the current on the thin domain is shown to converge in an appropriate sense to the current on the graph. Much can be said about the limiting problem on the graph; in particular, while on a circle, there is a simple criterion that relates the phase of a minimizer of the energy to the flux of the exterior magnetic field, there is no such simple criterion in the multiply connected domain case.
TUESDAY, April 8, 2003