Periodic unfolding and homogenization for the ginzburg-landau equation preliminary draft (904).

Content Provider	CiteSeerX
Author	Sauvageot, Myrto
Abstract	Abstract. We investigate, on a bounded domain Ω of R2 with fixed S1-valued boundary condition g of degree d> 0, the asymptotic behaviour of solutions uε,δ of a class of Ginzburg-Landau equations driven by two parameter: the usual Ginzburg-Landau parameter, denoted ε, and the scale parameter δ of a geometry provided by a field of 2 × 2 positive definite matrices x → A ( x δ). The field R2 ∋ x → A(x) is of class W 2, ∞ and periodic. We show, for a suitable choice of the ε’s depending on δ, the existence of a limit configuration u ∞ ∈ H1 g (Ω, S1), which, out of a finite set of singular points, is a weak solution of the equation of S1-valued harmonic functions for the geometry related to the usual homogenized matrix A0.
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Subject Keyword	Ginzburg-landau Equation Preliminary Draft Periodic Unfolding Homogenization Weak Solution S1-valued Harmonic Function Asymptotic Behaviour Scale Parameter Usual Ginzburg-landau Parameter Usual Homogenized Matrix A0 Field R2 Finite Set Singular Point Limit Configuration H1 Ginzburg-landau Equation Suitable Choice Fixed S1-valued Boundary Condition Bounded Domain Positive Definite Matrix
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Resource Type	Article