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arXiv · 2411.09498

Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility

Aaron Brunk·Marvin Fritz
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Abstract

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.

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Aaron Brunk, Marvin Fritz. 2024-11-14. Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility. https://doi.org/10.1007/s42985-025-00362-x

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