Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard equations, have been widely used to investigate interfacial dynamic problems. Designing accurate, efficient, stable numerical algorithms for solving phase models has an active decades. In this paper, we focus on using deep neural network design automatic solver equations by proposing improved physics informed (PINN). Thoug...

The Mullins Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn Hilliard equation. We show that classical solutions exist globally and tend to spheres exponentially fast, provided that they are close to a sphere initially. Our analysis is based on center manifold theory and on maximal regularity. 1998 Academic Press

We numerically investigate the influence of a homogeneous shear flow on the spinodal decomposition of a binary mixture by solving the Cahn-Hilliard equation in a two-dimensional geometry. Several aspects of this much studied problem are clarified. Our numerical data show unambiguously that, in the shear flow, the domains have on average an elliptic shape. The time evolution of the three paramet...

We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the nonlinearity cannot be neglected anymore, and before the coalescence dominates. The dynamics is captured through the standard technique of a solubility condition performed over a particular family of quasistatic...

We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar soluti...

We prove theorems characterizing the minimizers in a model for condensation based on the Cahn–Hilliard free energy functional. In particular we exactly determine the critical density for droplet formation.

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