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. "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 10-B.3 (2007): 1125-1142. <http://eudml.org/doc/290378>.

@article{Raguž2007,
abstract = {In this note we consider the Ginzburg-Landau functional \begin\{equation*\}I^\epsilon\_a(v) = \int\_0^1(\epsilon^2 v''^2(s) + W(v'(s)) + a(\epsilon^\{-\beta\}s(v^2(s)) \, ds\end\{equation*\} 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.},
author = {Raguž, Andrija},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {1125-1142},
publisher = {Unione Matematica Italiana},
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},
url = {http://eudml.org/doc/290378},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Raguž, Andrija
TI - A Note on Calculation of Asymptotic Energy for a Functional of Ginzburg-Landau Type with Externally Imposed Lower-Order Oscillatory Term in One Dimension
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 1125
EP - 1142
AB - In this note we consider the Ginzburg-Landau functional \begin{equation*}I^\epsilon_a(v) = \int_0^1(\epsilon^2 v''^2(s) + W(v'(s)) + a(\epsilon^{-\beta}s(v^2(s)) \, ds\end{equation*} 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.
LA - eng
UR - http://eudml.org/doc/290378
ER -