Long time behavior of higher-order anisotropic perturbed phase field system with regular potentials

Abstract

The aim of this article is to study asymptotic behavior of higher-order (in space) anisotropic perturbed Caginalp phase-field systems with relaxations hyperbolic in term of attractors. The main difficulty comes from the fact that the phase spaces for the perturbed ([Formula: see text]) and unperturbed ([Formula: see text]) equations are not the same; indeed, the limit problem is parabolic. Therefore, the previous approach employing for parabolic systems, cannot be applied and have to be adapted. In particular, this necessitates a study of the time boundary layer in order to estimate the difference of solutions between the perturbed and unperturbed equations. Finally, we obtain the existence of the global attractor, as well as the existence of exponential attractors.