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Convergence of exponential attractors for a time splitting approximation of the Caginalp phase-field system

  • * Corresponding author: M. Pierre

    * Corresponding author: M. Pierre
This work has been partially supported by the Fédération MIRES.
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  • We consider a time semi-discretization of the Caginalp phase-field model based on an operator splitting method. For every time-step parameter $ \tau $, we build an exponential attractor $ \mathcal{M}_\tau $ of the discrete-in-time dynamical system. We prove that $ \mathcal{M}_\tau $ converges to an exponential attractor $\mathcal{M}_0$ of the continuous-in-time dynamical system for the symmetric Hausdorff distance as $ \tau $ tends to $0$. We also provide an explicit estimate of this distance and we prove that the fractal dimension of $ \mathcal{M}_\tau $ is bounded by a constant independent of $ \tau $.

    Mathematics Subject Classification: Primary:37L30, 65M12;Secondary:35B41, 80A22.


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