@article{Batangouna2022, 
author = {Narcisse Batangouna},
title = {A robust family of exponential attractors for a time semi-discretization of the Ginzburg-Landau equation},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {1399-1415},
keywords = {Allen-Cahn equation, Ginzburg-Landau equation, exponential attractor, global attractor, backward Euler scheme},
url = {https://www.sciopen.com/article/10.3934/math.2022082},
doi = {10.3934/math.2022082},
abstract = {We consider a time semidiscretization of the Ginzburg-Landau equation by the backward Euler scheme. For each time step    τ, we build an exponential attractor of the dynamical system associated to the scheme. We prove that, as    τ tends to    0, this attractor converges for the symmetric Hausdorff distance to an exponential attractor of the dynamical system associated to the Allen-Cahn equation. We also prove that the fractal dimension of the exponential attractor and of the global attractor is bounded by a constant independent of    τ.}
}