Glasnik Matematicki, Vol. 44, No.2 (2009), 401-421.

A RESULT IN ASYMPTOTIC ANALYSIS FOR THE FUNCTIONAL OF GINZBURG-LANDAU TYPE WITH EXTERNALLY IMPOSED MULTIPLE SMALL SCALES IN ONE DIMENSION

Andrija Raguž

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: andrija@math.hr

Abstract.   In this paper we present technical improvement of results in our previous paper. We study asymptotic behavior of the functional

{\cal J}^{\vep}_{a,\beta,\gamma}(v)=\avv{0}{1}\Big({\vep}^2 v''^2(s)+W(v'(s))+a(\vep^{-\beta}s,\vep^{-\gamma}s)v^2(s)\Big)ds

as ε → 0, where a is 1 × 1-periodic. We determine (rescaled) minimal asymptotic energy associated to Jεa,β,γ as ε → 0 where β, γ ≥ 0, β + γ > 0.

2000 Mathematics Subject Classification.   34E15, 49J45.

Key words and phrases.   Minimization, multiple small scales, Ginzburg-Landau functional, Gamma convergence.

Full text (PDF) (free access)

DOI: 10.3336/gm.44.2.09

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