Glasnik Matematicki, Vol. 41, No.1 (2006), 89-99.

A NOTE ON CALCULATION OF ASYMPTOTIC ENERGY FOR GINZBURG-LANDAU FUNCTIONAL WITH ε-DEPENDENT 1-LIPSCHITZ PENALIZING TERM IN ONE DIMENSION

Andrija Raguž

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

Abstract.   We study asymptotic behavior of the Ginzburg-Landau functional

I^{\vep}_{g_{\vep}}(v)=\int_{\Omega}\Big({\vep}^2 v''^2(s)+W(v'(s))+a(s)(v(s)+g_{\vep}(s))^2\Big)ds

as ε → 0, where (gε) is a given sequence of 1-Lipschitz functions. In cases where the sequence (gε) possesses some additional properties we calculate (rescaled) minimal macroscopic energy associated to Iεgε as ε → 0. Thus we obtain partial generalization of our previous results.

2000 Mathematics Subject Classification.   34E15, 49J45.

Key words and phrases.   Young measures, relaxation, Ginzburg-Landau functional, Gamma convergence.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.09

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