Garcke, Harald and Lam, Kei Fong and Nuernberg, Robert and Signori, Andrea (2024) Complex pattern formation governed by a Cahn-Hilliard-Swift-Hohenberg system: Analysis and numerical simulations. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 34 (11). pp. 2055-2097. ISSN 0218-2025, 1793-6314
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This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting system leads to complex patterns involving a separation into phases as typical of the Cahn-Hilliard equation and small scale stripes and dots as seen in the Swift-Hohenberg equation. We introduce singular potentials of logarithmic type to enhance the model's accuracy in adhering to essential physical constraints. The paper establishes the existence and uniqueness of weak solutions within this extended framework. The insights gained contribute to a deeper understanding of phase separation in complex systems, with potential applications in materials science and related fields. We introduce a stable finite element approximation based on an obstacle formulation. Subsequent numerical simulations demonstrate that the model allows for complex structures as seen in pigment patterns of animals and in porous polymeric materials.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PHASE FIELD MODEL; FINITE-ELEMENT APPROXIMATION; COUPLED GINZBURG-LANDAU; STRATEGIES; EQUATIONS; Cahn-Hilliard-Swift-Hohenberg equation; phase separation; pattern formation; materials science; singular potentials; well-posedness; numerical simulations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 Oct 2025 06:35 |
| Last Modified: | 29 Oct 2025 06:35 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64692 |
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