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A result in asymptotic analysis for the functional of Ginzburg-Landau type with externally imposed multiple small scales in one dimension

In this paper we present technical improvement of resultsin [19]. We study asymptotic behavior of the functionalJεa ; β ; γ(v) =−Z10ε2v′′2(s) +W(v′(s)) +a(ε−βs ; ε−γs)v2(s)dsasε−→0, whereais 1×1-periodic. We determine (rescaled) minimalasymptotic energy associated toJεa ; β ; γasε−→0 whereβ ; γ≥0, β+γ >0.

Minimization, multiple small scales, Ginzburg-Landau functional, Gamma convergence

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