Minisymposium: Calculs rigoureux en systèmes dynamiques
Co-existence of non trivial solutions of the Ginzburg-Landau equation: a computer-assisted proof
Correc, Anaïs
Université Laval

A method based on Chebyshev series to rigorously compute solutions of the Ginzburg-Landau equation is proposed. The idea is to recast solutions as fixed points of an operator defined on a Banach space of rapidly decaying Chebyshev coefficients and to combine analytic estimates and the contraction mapping theorem to show the existence of a unique genuine solution nearby an approximate solution. With this approach, it is possible to answer some open questions regarding the co-existence of non trivial solutions of the Ginzburg-Landau model of superconductivity. This is joint work with J.-P. Lessard (U. Laval).

Mardi, 18 juin, 17h00
Salle Des Plaines A