A Note on Calculation of Asymptotic Energy for a Functional of Ginzburg-Landau Type with Externally Imposed Lower-Order Oscillatory Term in One Dimension

Raguž, Andrija

Raguž, Andrija

Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 1125-1142 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

In this note we consider the Ginzburg-Landau functional $I^{\epsilon}_{a}(v)=\int_{0}^{1}(\epsilon^{2}v^{\prime\prime 2}(s)+W(v^{\prime% }(s))+a(\epsilon^{-\beta}s(v^{2}(s))\,ds$ where $\beta>0$ and a is 1-periodic. We determine how (rescaled) minimal asymptotic energy associated to $I^{\epsilon}_{a}$ depends on parameter $\beta>0$ as $\epsilon\o 0$ . In particular, our analysis shows that minimizers of $I_{a}^{\epsilon}$ are nearly $\epsilon^{1/3}$ -periodic.

In questa nota consideriamo il funzionale di Ginzburg-Landau $I^{\epsilon}_{a}(v)=\int_{0}^{1}(\epsilon^{2}v^{\prime\prime 2}(s)+W(v^{\prime% }(s))+a(\epsilon^{-\beta}s(v^{2}(s))\,ds$ ove $\beta>0$ e $a$ è 1-periodica. Mostreremo come la minima energia asintotica (ridimensionata) associata a $I^{\epsilon}_{a}$ dipenda dal parametro $\beta>0$ per $\epsilon\to 0$ . In particolare, la nostra analisi mostra che i minimizzatori di $I^{\epsilon}_{a}$ sono quasi $\epsilon^{1/3}$ -periodici.

Publié le : 2007-10-01

Zbl 1189.49019

@article{BUMI_2007_8_10B_3_1125_0,
     author = {Andrija Ragu\v z},
     title = {A Note on Calculation of Asymptotic Energy for a Functional of Ginzburg-Landau Type with Externally Imposed Lower-Order Oscillatory Term in One Dimension},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {1125-1142},
     zbl = {1189.49019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_1125_0}
}

Raguž, Andrija. A Note on Calculation of Asymptotic Energy for a Functional of Ginzburg-Landau Type with Externally Imposed Lower-Order Oscillatory Term in One Dimension. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 1125-1142. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_1125_0/

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