@article{Chen2023, 
author = {Ko-Shin Chen and Cyrill Muratov and Xiaodong Yan},
title = {Layered solutions for a nonlocal Ginzburg-Landau model with periodic modulation},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {5},
pages = {1-52},
keywords = {layered solutions, nonlocal Ginzburg-Landau, periodic modulation},
url = {https://www.sciopen.com/article/10.3934/mine.2023090},
doi = {10.3934/mine.2023090},
abstract = {We study layered solutions in a one-dimensional version of the scalar Ginzburg-Landau equation that involves a mixture of a second spatial derivative and a fractional half-derivative, together with a periodically modulated nonlinearity. This equation appears as the Euler-Lagrange equation of a suitably renormalized fractional Ginzburg-Landau energy with a double-well potential that is multiplied by a 1-periodically varying nonnegative factor    g  (  x  ) with        ∫    0    1        1          g      (      x      )        d  x  <  ∞  . A priori this energy is not bounded below due to the presence of a nonlocal term in the energy. Nevertheless, through a careful analysis of a minimizing sequence we prove existence of global energy minimizers that connect the two wells at infinity. These minimizers are shown to be the classical solutions of the associated nonlocal Ginzburg-Landau type equation.}
}