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| In recent years, the so-called phase-field crystal (PFC) approach has been recently employed to model and simulate the dynamics of crystalline materials, including, e.g., crystal growth in a supercooled liquid, dendritic and eutectic solidification, epitaxial growth. We consider a modification of the so-called (sixth order) PFC equation introduced by K.R. Elder et al. This variant has recently been proposed by P. Stefanovic et al. to distinguish between elastic relaxation and diffusion time scales. It consists of adding an inertial term (i.e. a second-order time derivative) into the PFC equation. We present some results regarding well-posedness, regularity and longtime behavior obtained in collaboration with Hao Wu (Fudan University). |
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