Open AccessA robust family of exponential attractors for a time semi-discretization of the Ginzburg-Landau equation
Author(s) -
Narcisse Batangouna
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022082
Subject(s) - attractor , hausdorff dimension , mathematics , exponential function , exponential decay , bounded function , fractal dimension , discretization , euler's formula , constant (computer programming) , mathematical analysis , mathematical physics , dimension (graph theory) , hausdorff space , fractal , pure mathematics , physics , quantum mechanics , computer science , programming language
We consider a time semidiscretization of the Ginzburg-Landau equation by the backward Euler scheme. For each time step $ \tau $, we build an exponential attractor of the dynamical system associated to the scheme. We prove that, as $ \tau $ 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 $ \tau $.