Garcke, Harald and Knopf, Patrik and Nuernberg, Robert and Zhao, Quan (2023) A Diffuse-Interface Approach for Solid-State Dewetting with Anisotropic Surface Energies. JOURNAL OF NONLINEAR SCIENCE, 33 (2): 34. ISSN 0938-8974, 1432-1467
Full text not available from this repository. (Request a copy)Abstract
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in R-d for d is an element of {2,3}. The introduced model consists of the anisotropic Cahn-Hilliard equation, with either a smooth or a double-obstacle potential, together with a degenerate mobility function and appropriate boundary conditions on the wall. Upon regularizing the introduced diffuse-interface model, and with the help of suitable asymptotic expansions, we recover as the sharp-interface limit the anisotropic surface diffusion flow for the interface together with an anisotropic Young's law and a zero-flux condition at the contact line of the interface with a fixed external boundary. Furthermore, we show the existence of weak solutions for the regularized model, for both smooth and obstacle potential. Numerical results based on an appropriate finite element approximation are presented to demonstrate the excellent agreement between the proposed diffuse-interface model and its sharp-interface limit.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD EQUATION; PHASE-FIELD MODEL; FINITE-ELEMENT APPROXIMATION; GEOMETRIC EVOLUTION-EQUATIONS; SHARP; MOTION; FILMS; CURVATURE; EXISTENCE; DYNAMICS; Solid-state dewetting; Cahn-Hilliard equation; Anisotropy; Sharp-interface limit; Weak solutions; Finite element method |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Mar 2024 09:03 |
| Last Modified: | 05 Mar 2024 09:03 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59277 |
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