engleski

On stability of asymptotic energy for a functional of the Ginzburg-Landau type with epsilon-dependent weakly-star convergent 1- Lipschitz penalizing term

We apply the approach developed in the paper G. Alberti, S. Müller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761-825 (2001) to calculate rescaled asymptotic energy associated to certain Ginzburg- Landau functional in one dimension. We generalize results from the paper A. Raguž: Relaxation of Ginzburg-Landau functional with 1-Lipschitz penalizing term in one dimension by Young measures on micropatterns, Asymptotic Anal. 41(3, 4), 331- 361 (2005), where original functional was penalized by 1-Lipschitz function g. In this note we consider the case when such penalizing functions depend on small parameter ε as their derivatives oscillate with period equal to ε to the power of γ for someγ > 0. We show that there are three distinctive cases of γ which lead to different asymptotic energy.

Singular perturbation, Ginzburg-Landau functional

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