Higher-order anisotropic models in phase separation

Abstract

Our aim in this paper is to study higher-order (in space) Allen–Cahn and Cahn–Hilliard models. In particular, we obtain well-posedness results, as well as the existence of the global attractor. We also give, for the Allen–Cahn models, numerical simulations which illustrate the effects of the higher-order terms and the anisotropy.

Keywords

• allen–cahn model
• cahn–hilliard model
• higher-order models
• anisotropy
• well-posedness
• dissipativity
• global attractor
• numerical simulations
• 35k55
• 35j60