| Issue |
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
|
|
|---|---|---|
| Page(s) | 1755 - 1783 | |
| DOI | https://doi.org/10.1051/m2an/2024061 | |
| Published online | 23 September 2024 | |
A robust family of exponential attractors for a linear time discretization of the Cahn-Hilliard equation with a source term
1
Laboratoire de Mathématiques et Applications, Université de Poitiers, CNRS, 86073 Poitiers, France
2
Universite d’Etat d’Haiti, Ecole Normale Superieure, Laboratoire de Mathematiques et Applications (LAMA-UEH), HT6115, 2 Rue Caseus, Pacot, Port-au-Prince, Haiti
* Corresponding author: Morgan.Pierre@math.univ-poitiers.fr; morgan.pierre@univ-poitiers.fr
Received:
24
August
2023
Accepted:
28
July
2024
We consider a linear implicit-explicit (IMEX) time discretization of the Cahn-Hilliard equation with a source term, endowed with Dirichlet boundary conditions. For every time step small enough, we build an exponential attractor of the discrete-in-time dynamical system associated to the discretization. We prove that, as the time step tends to 0, this attractor converges for the symmetric Hausdorff distance to an exponential attractor of the continuous-in-time dynamical system associated with the PDE. We also prove that the fractal dimension of the exponential attractor (and consequently, of the global attractor) is bounded by a constant independent of the time step. The results also apply to the classical Cahn-Hilliard equation with Neumann boundary conditions.
Mathematics Subject Classification: 37L30 / 65M12
Key words: Cahn-Hilliard equation / source term / exponential attractor / global attractor / IMEX scheme
© The authors. Published by EDP Sciences, SMAI 2024
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