Robust exponential attractors for the modified phase-field crystal equation

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 $\beta {\varphi }_{tt}$. Here $\varphi$ is the phase function standing for the number density of atoms and $\beta \ge 0$ 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 Hölder continuous with respect to $\beta$.

arXiv admin note: text overlap with arXiv:1306.5857

References in corpus (2)

• Modeling Elasticity in Crystal Growth
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview