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Robust exponential attractors for the modified phase-field crystal equation

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 $βϕ_{tt}$. Here $ϕ$ is the phase function standing for the number density of atoms and $β\geq 0$ is a relaxation time. The associated dynamical system for the MPFC equation with respect to the parameter $β$ is analyzed. More precisely, we establish the existence of a family of exponential attractors $\mathcal{M}_β$ that are Hölder continuous with respect to $β$.