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arXiv · 1312.2834

Robust exponential attractors for the modified phase-field crystal equation

Maurizio Grasselli·Hao Wu
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Abstract

We consider the modified phase-field crystal (MPFC) equation that has recently been proposed by P. Stefanovic et al. This is a variant of the phase-field crystal (PFC) equation, introduced by K.-R. Elder et al., which is characterized by the presence of an inertial term $\beta\phi_{tt}$. Here $\phi$ is the phase function standing for the number density of atoms and $\beta\geq 0$ is a relaxation time. The associated dynamical system for the MPFC equation with respect to the parameter $\beta$ is analyzed. More precisely, we establish the existence of a family of exponential attractors $\mathcal{M}_\beta$ that are H\"older continuous with respect to $\beta$.

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Maurizio Grasselli, Hao Wu. 2013-12-10. Robust exponential attractors for the modified phase-field crystal equation. https://arxiv.org/abs/1312.2834

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