Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915773339926528 |
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| author | Brunk, Aaron Fritz, Marvin |
| author_facet | Brunk, Aaron Fritz, Marvin |
| contents | The Ohta-Kawasaki equation models the mesoscopic phase separation of immiscible polymer chains that form diblock copolymers, with applications in directed self-assembly for lithography. We perform a mathematical analysis of this model under degenerate mobility and an external force, proving the existence of weak solutions via an approximation scheme for the mobility function. Additionally, we propose a fully discrete scheme for the system and demonstrate the existence and uniqueness of its discrete solution, showing that it inherits essential structural-preserving properties. Finally, we conduct numerical experiments to compare the Ohta-Kawasaki system with the classical Cahn-Hilliard model, highlighting the impact of the repulsion parameter on the phase separation dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility Brunk, Aaron Fritz, Marvin Numerical Analysis Analysis of PDEs The Ohta-Kawasaki equation models the mesoscopic phase separation of immiscible polymer chains that form diblock copolymers, with applications in directed self-assembly for lithography. We perform a mathematical analysis of this model under degenerate mobility and an external force, proving the existence of weak solutions via an approximation scheme for the mobility function. Additionally, we propose a fully discrete scheme for the system and demonstrate the existence and uniqueness of its discrete solution, showing that it inherits essential structural-preserving properties. Finally, we conduct numerical experiments to compare the Ohta-Kawasaki system with the classical Cahn-Hilliard model, highlighting the impact of the repulsion parameter on the phase separation dynamics. |
| title | Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2411.09498 |