Garcke, Harald and Knopf, Patrik and Signori, Andrea (2025) The anisotropic Cahn-Hilliard equation with degenerate mobility: Existence of weak solutions. ANALYSIS AND APPLICATIONS. ISSN 0219-5305, 1793-6861
Full text not available from this repository. (Request a copy)Abstract
This paper presents an existence result for the anisotropic Cahn-Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account an anisotropic energy. The model allows for the degeneracy of the mobility at specific concentration values, demonstrating that the solution remains within physically relevant bounds. The introduction of anisotropy leads to highly nonlinear terms making energy and entropy estimates rather involved. As the mobility degenerates in the pure phases, the degenerate Cahn-Hilliard equation describes surface diffusion and is an important model to model solid-state dewetting (SSD) of thin films. We show existence of weak solutions for the anisotropic degenerate Cahn-Hilliard equation by using suitable energy- and entropy-type estimates.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SHARP; MOTION; Anisotropic Cahn-Hilliard equation; phase transition; weak solutions; degenerate mobility; anisotropic energy |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Apr 2026 06:02 |
| Last Modified: | 15 Apr 2026 06:02 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66268 |
Actions (login required)
 |
View Item |
