engleski

A note on calculation of asymptotic energy for Ginzburg-Landau functional with externally imposed lower-order oscillatory term in one dimension

In this note we consider the Ginzburg-Landau functional equipped with highly oscillatory periodic lower order term with $\varepsilon^{; ; ; \beta}; ; ; $-periodic penalizing function, where $\beta>0$ and $varepsilon\approx 0$. We determine how the corresponding rescaled aymptotic energy depends on the parameter $\beta$ as $\varepsilon$ tends to zero. In particuler, our analysis shows that minimizers of such a class of functionals are nearly $\varepsilon^{; ; ; 1\slash 3}; ; ; $-periodic.

Ginzburg-Landau functional ; Gamma-convergence ; penalization

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